This HTML5 document contains 824 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dbpedia-bghttp://bg.dbpedia.org/resource/
dbpedia-cshttp://cs.dbpedia.org/resource/
freebasehttp://rdf.freebase.com/ns/
n91http://blog.plover.com/math/
dbpedia-dehttp://de.dbpedia.org/resource/
dbpedia-svhttp://sv.dbpedia.org/resource/
n68https://www.ams.org/notices/200604/
dbpedia-plhttp://pl.dbpedia.org/resource/
dbpedia-pthttp://pt.dbpedia.org/resource/
yagohttp://dbpedia.org/class/yago/
n39https://link.springer.com/book/
n80https://books.google.com/
n65http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/
dbpedia-thhttp://th.dbpedia.org/resource/
dbpedia-hrhttp://hr.dbpedia.org/resource/
dbpedia-simplehttp://simple.dbpedia.org/resource/
dbpedia-cahttp://ca.dbpedia.org/resource/
n72https://www.ams.org/bull/1980-03-02/S0273-0979-1980-14832-6/
dbpedia-idhttp://id.dbpedia.org/resource/
xsdhhttp://www.w3.org/2001/XMLSchema#
n53http://hi.dbpedia.org/resource/
dbpedia-ukhttp://uk.dbpedia.org/resource/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
n44https://arxiv.org/abs/cs/
dbrhttp://dbpedia.org/resource/
dbpedia-nlhttp://nl.dbpedia.org/resource/
n94https://www.webcitation.org/6gQ72rSwF%3Furl=http:/www.textarchiv.homepage.bluewin.ch/Antinomien/
dbpedia-eohttp://eo.dbpedia.org/resource/
n55http://www.godelbook.net/
dbpedia-ithttp://it.dbpedia.org/resource/
dbpedia-arhttp://ar.dbpedia.org/resource/
dbphttp://dbpedia.org/property/
dcthttp://purl.org/dc/terms/
dbpedia-frhttp://fr.dbpedia.org/resource/
n16http://my.dbpedia.org/resource/
dbpedia-fahttp://fa.dbpedia.org/resource/
n41http://www.radiolab.org/story/161758-break-cycle/
dbpedia-kahttp://ka.dbpedia.org/resource/
n22http://ur.dbpedia.org/resource/
n47http://pa.dbpedia.org/resource/
dbpedia-skhttp://sk.dbpedia.org/resource/
n67http://scn.dbpedia.org/resource/
n25http://plato.stanford.edu/entries/logic-paraconsistent/
n85https://www.cairn.info/
dbpedia-alshttp://als.dbpedia.org/resource/
goldhttp://purl.org/linguistics/gold/
n15http://d-nb.info/gnd/
dbpedia-fihttp://fi.dbpedia.org/resource/
n79http://people.ucalgary.ca/~rzach/static/
n40http://ast.dbpedia.org/resource/
n82https://web.archive.org/web/20040916041216/http:/www.research.ibm.com/people/h/hirzel/papers/
dbpedia-glhttp://gl.dbpedia.org/resource/
dbthttp://dbpedia.org/resource/Template:
dbpedia-dahttp://da.dbpedia.org/resource/
dbpedia-zhhttp://zh.dbpedia.org/resource/
owlhttp://www.w3.org/2002/07/owl#
n62https://global.dbpedia.org/id/
dbpedia-srhttp://sr.dbpedia.org/resource/
n14https://philarchive.org/rec/
dbchttp://dbpedia.org/resource/Category:
n29http://bs.dbpedia.org/resource/
dbpedia-elhttp://el.dbpedia.org/resource/
n49http://www.realviewbooks.com/
dbpedia-hehttp://he.dbpedia.org/resource/
n84http://cv.dbpedia.org/resource/
n52http://opus.ipfw.edu/cgi/
n10https://www.isa-afp.org/entries/
dbpedia-kohttp://ko.dbpedia.org/resource/
dbpedia-ethttp://et.dbpedia.org/resource/
n23http://www.math.ias.edu/~avi/BOOKS/
n36https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/
n69http://podnieks.id.lv/
wikidatahttp://www.wikidata.org/entity/
foafhttp://xmlns.com/foaf/0.1/
dbpedia-gahttp://ga.dbpedia.org/resource/
n18https://projecteuclid.org/euclid.lnl/
dbpedia-lahttp://la.dbpedia.org/resource/
dbpedia-huhttp://hu.dbpedia.org/resource/
dbpedia-eshttp://es.dbpedia.org/resource/
dbpedia-ruhttp://ru.dbpedia.org/resource/
n30http://kn.dbpedia.org/resource/
dbpedia-vihttp://vi.dbpedia.org/resource/
dbpedia-iohttp://io.dbpedia.org/resource/
rdfshttp://www.w3.org/2000/01/rdf-schema#
dbpedia-nohttp://no.dbpedia.org/resource/
n21http://www.research.ibm.com/people/h/hirzel/papers/
n38https://plato.stanford.edu/entries/goedel-incompleteness/
provhttp://www.w3.org/ns/prov#
dbohttp://dbpedia.org/ontology/
dbpedia-jahttp://ja.dbpedia.org/resource/
dbpedia-trhttp://tr.dbpedia.org/resource/
dbpedia-nnhttp://nn.dbpedia.org/resource/
n58http://aleph0.clarku.edu/~djoyce/hilbert/
wikipedia-enhttp://en.wikipedia.org/wiki/
n42https://arxiv.org/abs/math/

Statements

Subject Item
dbr:Principia_Mathematica
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Proof_of_impossibility
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Proof_sketch_for_Gödel's_first_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Quantum_mind
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:List_of_first-order_theories
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Model_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Murasaki_(novel)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Löb's_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Metalogic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Metatheory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Paris–Harrington_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:David_Hilbert
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Decider_(Turing_machine)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Anti-realism
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:History_of_artificial_intelligence
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:History_of_the_function_concept
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:John_von_Neumann
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:List_of_Dutch_inventions_and_innovations
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Arithmetization_of_syntax
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Peano_axioms
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Reverse_mathematics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Curry's_paradox
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:David_Corfield
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:David_Wolpert
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Incompressibility_method
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Index_of_epistemology_articles
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Index_of_philosophy_articles_(D–H)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Infinity_and_the_Mind
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Interesting_number_paradox
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Liar_paradox
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:List_of_important_publications_in_mathematics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:List_of_incomplete_proofs
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:List_of_mathematical_logic_topics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:List_of_scientific_laws_named_after_people
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Richard_Jeffrey
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Penrose–Lucas_argument
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Power_of_a_method
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Systems_of_Logic_Based_on_Ordinals
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:The_Age_of_Spiritual_Machines
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Pseudomathematics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Kurt_Godel's_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Kurt_Goedel's_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Consistency
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:An_Introduction_to_the_Philosophy_of_Mathematics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Mathematical_logic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Mathematicism
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Mathematics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Max_Newman
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Omnipotence_paradox
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Second_Conference_on_the_Epistemology_of_the_Exact_Sciences
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Elliptic_geometry
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Frank_Ramsey_(mathematician)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:George_Boolos
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Glossary_of_set_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Mu_(negative)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Naive_set_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Constructive_set_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Continuum_hypothesis
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Thoralf_Skolem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Dan_Willard
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Orchestrated_objective_reduction
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Uncle_Petros_and_Goldbach's_Conjecture
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Bew
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Stanisław_Świerczkowski
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Stephen_Cole_Kleene
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Strange_loop
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Stuart_Hameroff
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Completeness_(logic)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Computable_set
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Francisco_Dória
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Full-employment_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Ignoramus_et_ignorabimus
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Leon_Henkin
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Principle_of_sufficient_reason
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Typographical_Number_Theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Mathematical_Cranks
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Mathematical_software
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Mediology
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:To_Mock_a_Mockingbird
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Actor–network_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Thought
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Through_the_Wormhole
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Truth
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Darwin's_Angel
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Walter_Benjamin
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Disjunction_and_existence_properties
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_completeness_theorem
owl:differentFrom
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_β_function
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel,_Escher,_Bach
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel_machine
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel_numbering
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Logical_intuition
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Robinson_arithmetic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Non-standard_model_of_arithmetic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:20th_century
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Ada_Lovelace
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Alain_Badiou
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Alfred_North_Whitehead
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Alfred_Tarski
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Darwin's_Dangerous_Idea
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Ernest_Nagel
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Fallibilism
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Finite_set
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:First_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Formalism_(philosophy_of_mathematics)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Barber_paradox
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Brouwer–Heyting–Kolmogorov_interpretation
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Catuṣkoṭi
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Causal_decision_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Diagonal_lemma
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Formal_system
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Foundations_of_mathematics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Grammatical_Man
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Hilbert's_program
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Hilbert's_second_problem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:History_of_computer_science
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:History_of_logic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Ludwig_Wittgenstein's_philosophy_of_mathematics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Proof_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Quine's_paradox
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Reductionism
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Relation_algebra
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_incompleteness_theorems
rdf:type
yago:Proposition106750804 owl:Thing yago:Statement106722453 yago:Theorem106752293 yago:Communication100033020 yago:Falsehood106756407 yago:WikicatParadoxes yago:Contradiction107206887 yago:WikicatTheoremsInTheFoundationsOfMathematics yago:WikicatTheorems yago:Abstraction100002137 yago:WikicatMathematicalTheorems yago:Paradox106724559 yago:Message106598915
rdfs:label
Теореми Геделя про неповноту 괴델의 불완전성 정리 Twierdzenia Gödla Cruthú Gödel Gödelovy věty o neúplnosti Θεωρήματα μη πληρότητας του Γκέντελ Teoremas de incompletitud de Gödel Gödel's incompleteness theorems Teoremas da incompletude de Gödel مبرهنات عدم الاكتمال لغودل Onvolledigheidsstellingen van Gödel Théorèmes d'incomplétude de Gödel Teorema d'incompletesa de Gödel 哥德尔不完备定理 Gödelscher Unvollständigkeitssatz Teoremoj de nekompleteco ゲーデルの不完全性定理 Teoremi di incompletezza di Gödel Теоремы Гёделя о неполноте Teorema ketaklengkapan Gödel Gödels ofullständighetssatser
rdfs:comment
Teorema ketaklengkapan Gödel (bahasa Inggris: Gödel's incompleteness theorems) adalah dua teorema logika matematika yang menetapkan batasan (limitation) inheren dari semua kecuali sistem aksiomatik yang paling trivial yang mampu mengerjakan aritmetika. Teorema-teorema ini, dibuktikan oleh Kurt Gödel pada tahun 1931, penting baik dalam logika matematika maupun dalam filsafat matematika. Kedua hasil ini secara luas, tetapi tidak secara universal, ditafsirkan telah menunjukkan bahwa program Hilbert untuk menghitung himpunan lengkap dan konsisten dari aksioma-aksioma bagi semua matematika adalah tidak mungkin, sehingga memberikan jawaban negatif terhadap soal Hilbert yang kedua. Gödelovy věty o neúplnosti jsou dvě důležité matematické věty, které mají zcela výsadní postavení v celé moderní matematické logice. Důležitou roli však hrají v celé matematice, zejména pak v teorii modelů, aritmetice (respektive teorii čísel) a v teorii množin. Dokázal je roku 1931 rakouský logik Kurt Gödel. Gödels ofullständighetsteorem är två fundamentala teorem inom den moderna logiken. De handlar om avgörbarhet och bevisbarhet av utsagor i formella system och lades fram av Kurt Gödel 1931. Teoremen fastlägger att Hilberts andra problem, om en axiomatisering av aritmetiken, kräver ett oändligt antal axiom. Det medför att David Hilberts program, att finna ett fullständigt och konsistent, det vill säga motsägelsefritt, axiomsystem för all matematik är ogenomförbart. Gödels första ofullständighetsteorem: Gödels andra ofullständighetsproblem, är en följdsats till det första teoremet: De onvolledigheidsstellingen van Gödel zijn twee stellingen over de beperkingen van formele systemen, beide bewezen door Kurt Gödel in 1931. Door deze onvolledigheidsstellingen gaf Gödel het platonisme binnen de wiskunde een nieuw elan. Στη μαθηματική λογική, τα θεωρήματα μη πληρότητας του Γκέντελ, τα οποία αποδείχτηκαν από τον Κουρτ Γκέντελ (Kurt Gödel) το 1931, αποτελούν δύο θεωρήματα που υποδεικνύουν έμφυτους περιορισμούς σε όλα τα (πλην των τετριμμένων) τυπικά συστήματα των μαθηματικών. Τα θεωρήματα είναι πολύ σημαντικά για τη φιλοσοφία των μαθηματικών. Ερμηνεύονται γενικά ως μια απόδειξη πως το να βρεθεί ένα πλήρες και συνεπές σύνολο από αξιώματα για όλα τα μαθηματικά είναι αδύνατο, δίνοντας έτσι αρνητική απάντηση στο . 在数理逻辑中,哥德尔不完备定理是库尔特·哥德尔于1931年证明并发表的两条定理。第一条定理指出: 这是形式逻辑中的定理,容易被错误表述。有许多命题听起来很像是哥德尔不完备定理,但事实上并不是。具体实例见。 把第一条定理的证明过程在体系内部形式化后,哥德尔证明了第二条定理。该定理指出: 哥德尔不完备定理破坏了希尔伯特计划的哲学企图。大卫·希尔伯特提出,像实分析那样较为复杂的体系的相容性,可以用较为简单的体系中的手段来证明。最终,全部数学的相容性都可以归结为基本算术的相容性。但哥德尔的第二条定理证明了基本算术的相容性不能在自身内部证明,因此当然就不能用来证明比它更强的系统的相容性了。 Теорема Геделя про неповноту і друга теорема Геделя (англ. Gödel's incompleteness theorems) — дві теореми математичної логіки про принципові обмеження формальної арифметики і, як наслідок, будь-якої формальної системи, в якій можливо визначити основні арифметичні поняття: натуральні числа, 0, 1, додавання та множення. Перша теорема стверджує, що, якщо формальна арифметика є несуперечливою, то в ній існує невивідна і неспростовна формула. Обидві ці теореми було доведено Куртом Геделем 1930 року (опубліковано 1931 року), вони мають безпосередній стосунок до зі знаменитого списку Гільберта. Les théorèmes d'incomplétude de Gödel sont deux théorèmes célèbres de logique mathématique, publiés par Kurt Gödel en 1931 dans son article (en) (« Sur les propositions formellement indécidables des Principia Mathematica et des systèmes apparentés »). Ils ont marqué un tournant dans l'histoire de la logique en apportant une réponse négative à la question de la démonstration de la cohérence des mathématiques posée plus de 20 ans auparavant par le programme de Hilbert. ゲーデルの不完全性定理(ゲーデルのふかんぜんせいていり、英: Gödel's incompleteness theorems、独: Gödelscher Unvollständigkeitssatz)または不完全性定理とは、数学基礎論とコンピュータ科学(計算機科学)の重要な基本定理。(数学基礎論は数理論理学や超数学とほぼ同義な分野で、コンピュータ科学と密接に関連している。) 不完全性定理は厳密には「数学」そのものについての定理ではなく、「形式化された数学」についての定理である。クルト・ゲーデルが1931年の論文で証明した定理であり、有限の立場(形式主義)では自然数論の無矛盾性の証明が成立しないことを示す。なお、少し拡張された有限の立場では、自然数論の無矛盾性の証明が成立する()。 「」および「ゲーデルの完全性定理」も参照 「」および「不完全性定理によるヒルベルト・プログラムの発展」も参照 مبرهنات عدم الاكتمال لغودل هما مبرهنتان في المنطق الرياضي برهنَ عليهما كورت غودل في عام 1931. وهما نظريتان تنصّان على حدود جميع الأنظمة الشكلية في الحساب.تعتبر هاتان النظريتان مهمتين في فلسفة الرياضيات، وتستخدمان لإثبات استحالة إيجاد مجموعة كاملة من البديهيات لكل علم الرياضيات ببرنامج هيلبرت، ممَّا يعطي جواباً سلبياً -بالتالي- . Twierdzenia Gödla – wspólna nazwa dwóch rezultatów logiki matematycznej i metamatematyki: * twierdzenie o niezupełności arytmetyki, * jego konsekwencja nazywana też twierdzeniem o niedowodliwości niesprzeczności. Los teoremas de incompletitud de Gödel son dos célebres teoremas de lógica matemática demostrados por Kurt Gödel en 1931. Ambos están relacionados con la existencia de proposiciones indecidibles en ciertas teorías aritméticas. Der Gödelsche Unvollständigkeitssatz ist einer der wichtigsten Sätze der modernen Logik. Er beschäftigt sich mit der Ableitbarkeit von Aussagen in formalen Systemen. Der Satz zeigt die Grenzen der formalen Systeme ab einer bestimmten Leistungsfähigkeit auf. Er weist nach, dass es in hinreichend starken Systemen, wie der Arithmetik, Aussagen geben muss, die man formal weder beweisen noch widerlegen kann. Der Satz beweist damit die Undurchführbarkeit des Hilbertprogramms, das von David Hilbert unter anderem begründet wurde, um die Widerspruchsfreiheit der Mathematik zu beweisen. Der Satz wurde 1931 von dem österreichischen Mathematiker Kurt Gödel veröffentlicht. La teoremoj de nekompleteco estas du teoremoj de matematika logiko pruvitaj de Kurt Gödel en 1930. Iomete simpligite, la unua teoremo asertas: En iu ajn de matematiko, en kiu eblas difini la aritmetikon de la naturaj nombroj, eblas konstrui propozicion, kiun oni povas nek pruvi nek malpruvi. La dua teoremo, kiun oni povas derivi el la unua, asertas: En iu ajn nekontraŭdira sistemo, en kiu eblas difini la aritmetikon de la naturaj nombroj, oni ne povas pruvi la nekontraŭdirecon de tiu sistemo mem. Os teoremas da incompletude de Gödel são dois teoremas da lógica matemática que estabelecem limitações inerentes a quase todos os sistemas axiomáticos, exceto aos mais triviais. Os teoremas, provados por Kurt Gödel em 1931, são importantes tanto para a lógica matemática quanto para a filosofia da matemática. Os dois resultados são amplamente, mas não universalmente, interpretados como indicações de que o programa de Hilbert para encontrar um conjunto completo e consistente de axiomas para toda a matemática é impossível, dando uma resposta negativa para o segundo problema de Hilbert. 괴델의 불완전성 정리(영어: Gödel’s incompleteness theorems)는 수리논리학에서 페아노 공리계를 포함하는 모든 무모순적 공리계는 참인 일부 명제를 증명할 수 없으며, 특히 스스로의 무모순성을 증명할 수 없다는 정리다. Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. In logica matematica, i teoremi di incompletezza di Gödel sono due famosi teoremi dimostrati da Kurt Gödel nel 1930. Gödel annunciò il suo primo teorema di incompletezza in una tavola rotonda a margine della Seconda Conferenza sull'Epistemologia delle Scienze esatte di Königsberg. John von Neumann, presente alla discussione, riuscì a dimostrare il teorema per conto suo verso la fine del 1930 e, inoltre, fornì una dimostrazione del secondo teorema di incompletezza, che annunciò a Gödel in una lettera datata 20 novembre 1930. Gödel aveva, nel frattempo, a sua volta ottenuto una dimostrazione del secondo teorema di incompletezza, e lo incluse nel manoscritto che fu ricevuto dalla rivista Monatshefte für Mathematik il 17 novembre 1930. Essi fanno parte dei teoremi limitativi, che precisano le Chruthaigh an matamaiticeoir Meiriceánach Kurt Gödel (1906-1978) i 1931 go mbíonn tairiscintí i gcónaí taobh istigh de bhrainse ar bith matamataice nach féidir a chruthú ná a bhréagnú le bunrialacha an bhrainse sin. Thaispeáin sé gur gá dul taobh amuigh den bhrainse ina leithéid de chás agus rialacha nua a leagan amach. Meastar uaidh sin nach féidir ríomhaire a dhéanamh chomh hintleachtach le daoine, de bhrí go mbionn an ríomhaire teoranta d'oiread ar leith rialacha a leagann an dearthóir amach dó, ach gur féidir le daoine coincheapanna is fírinní gan choinne a fháil amach i gcónaí. En lògica matemàtica, els teoremes d'incompletesa de Gödel són dos cèlebres teoremes demostrats per Kurt Gödel l'any 1930. Simplificant, el primer teorema afirma: En qualsevol formalització de les matemàtiques que sigui prou forta per definir el concepte de nombres naturals, es pot construir una afirmació que ni es pot demostrar ni es pot refutar dins d'aquest sistema. El segon teorema, que es demostra formalitzant part de la demostració del primer teorema dins el mateix sistema, afirma: Cap sistema consistent es pot usar per demostrar-se a si mateix. Теорема Гёделя о неполноте и вторая теорема Гёделя — две теоремы математической логики о принципиальных ограничениях формальной арифметики и, как следствие, всякой формальной системы, в которой можно определить основные арифметические понятия: натуральные числа, 0, 1, сложение и умножение. Первая теорема утверждает, что если формальная арифметика непротиворечива, то в ней существует невыводимая и неопровержимая формула. Вторая теорема утверждает, что если формальная арифметика непротиворечива, то в ней невыводима некоторая формула, содержательно утверждающая непротиворечивость этой арифметики.
rdfs:seeAlso
dbr:Hilbert–Bernays_provability_conditions dbr:List_of_statements_independent_of_ZFC dbr:Proof_sketch_for_Gödel's_first_incompleteness_theorem dbr:Halting_problem dbr:Automated_theorem_proving
dct:subject
dbc:Model_theory dbc:Works_by_Kurt_Gödel dbc:Epistemology dbc:Theorems_in_the_foundations_of_mathematics dbc:Proof_theory dbc:Mathematical_logic dbc:Metatheorems
dbo:wikiPageID
58863
dbo:wikiPageRevisionID
1124610774
dbo:wikiPageWikiLink
dbr:Synthese dbr:Bona_fide dbr:Complete_theory dbr:On_Formally_Undecidable_Propositions_in_Principia_Mathematica_and_Related_Systems_I dbr:Philosophia_Mathematica dbr:Logicism dbr:Gödel_number dbr:Von_Neumann_universe dbr:Essentially_undecidable dbr:Introduction_to_Automata_Theory,_Languages,_and_Computation dbr:Formal_system dbr:Quining dbr:The_Journal_of_Philosophy dbr:Theorem dbr:On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems dbr:Logica_Universalis dbr:Subset dbr:Ophelia_Benson dbr:Anti-realist dbr:Epsilon_calculus dbr:Saharon_Shelah dbr:Gentzen's_consistency_proof dbr:Turing_machine dbr:Computable_function dbr:Computably_enumerable dbr:Computability_theory dbr:Mathematical_Platonism dbr:Stewart_Shapiro dbr:Ω-consistent_theory dbr:Ernst_Zermelo dbr:Character_encoding dbr:Proof_theory dbr:Theory_of_everything dbr:Jeff_Paris_(mathematician) dbr:Natural_language dbr:Presburger_arithmetic dbr:James_R._Newman dbr:Proof_assistant dbr:Goodstein's_theorem dbr:Logically_valid dbr:Fashionable_Nonsense dbr:Alonzo_Church dbc:Model_theory dbr:Second_Conference_on_the_Epistemology_of_the_Exact_Sciences dbr:Martin_Davis_(mathematician) dbr:Effective_procedure dbr:Monatshefte_für_Mathematik_und_Physik dbr:Kurt_Gödel dbr:A._K._Peters dbr:Whitehead_problem dbr:Joseph_R._Shoenfield dbr:Independence_(mathematical_logic) dbr:Jean_van_Heijenoort dbr:Gerhard_Gentzen dbr:Church–Turing_thesis dbr:Löb's_Theorem dbr:Diagonal_lemma dbc:Works_by_Kurt_Gödel dbr:Hao_Wang_(academic) dbr:Syntax dbr:Undecidable_set dbr:John_Hopcroft dbr:Alfred_Tarski dbr:Rebecca_Goldstein dbr:Tarski's_undefinability_theorem dbr:R._B._Braithwaite dbr:Primitive_recursive_function dbr:David_Hilbert dbr:Sidney_Hook dbr:Proof_by_contradiction dbr:Wolfgang_Rautenberg dbr:Second-order_arithmetic dbr:Graph_minor_theorem dbc:Epistemology dbr:Decision_problem dbr:John_Lucas_(philosopher) dbr:Hilbert–Bernays_provability_conditions dbc:Theorems_in_the_foundations_of_mathematics dbr:Modus_ponens dbr:Ordinal_number dbr:Gregory_Chaitin dbr:Richard's_paradox dbr:Vienna_Circle dbr:Gottlob_Frege dbr:Stanford_Encyclopedia_of_Philosophy dbr:Hilbert's_program dbr:Hilbert's_second_problem dbr:Stephen_Hawking dbr:Crispin_Wright dbr:Rosser's_trick dbr:Primitive_recursive_arithmetic dbr:Paul_Bernays dbr:Typographical_Number_Theory dbr:Continuum_hypothesis dbr:Nachlass dbr:Real_closed_field dbr:Raymond_Smullyan dbr:Deductive_system dbr:True_arithmetic dbr:Paris–Harrington_theorem dbr:Algebraically_closed_field dbr:Inner_model dbr:Coq dbc:Proof_theory dbr:Habilitation dbr:Zermelo–Fraenkel_set_theory dbr:Completeness_theorem dbr:Jeffrey_Ullman dbr:Inaccessible_cardinal dbr:Symbolic_Logic dbr:John_Barkley_Rosser dbr:Robinson_arithmetic dbr:I_Am_a_Strange_Loop dbr:Karl_Menger dbr:Douglas_Hofstadter dbr:Ordinal_analysis dbr:Gödel_machine dbr:Gödel,_Escher,_Bach dbr:Gödel's_completeness_theorem dbr:Mathematics dbr:Principle_of_explosion dbr:Gödel's_speed-up_theorem dbr:Alan_Sokal dbr:Bertrand_Russell dbr:Consistency dbr:Natalie_Wolchover dbr:ASCII dbr:Association_for_Symbolic_Logic dbr:Chaitin's_incompleteness_theorem dbr:Régis_Debray dbr:Mathematical_logic dbr:Quanta_Magazine dbr:Truth_value dbr:Dialetheia dbr:Wilhelm_Ackermann dbc:Mathematical_logic dbr:Dialetheism dbr:Remarks_on_the_Foundations_of_Mathematics dbr:MRDP_theorem dbr:Gödel dbr:Berry's_paradox dbr:Ramsey_theorem dbr:Ludwig_Wittgenstein dbr:ZFC dbr:Geoffrey_Hellman dbr:Axiom_of_choice dbr:Juliet_Floyd dbr:Alan_Turing dbr:Model_theory dbr:Natarajan_Shankar dbr:Grundlagen_der_Mathematik dbr:Axiom dbr:HOL_Light dbr:Saul_Kripke dbr:Avi_Wigderson dbr:Minds,_Machines_and_Gödel dbr:Computational_complexity_theory dbr:Torkel_Franzén dbr:John_von_Neumann dbr:Contradiction dbr:Arithmetical_hierarchy dbr:Tarski's_indefinability_theorem dbr:Ideal_language_philosophy dbr:Philosophy_of_mathematics dbr:Provability_logic dbr:Tarski's_axioms dbr:Maximal_set dbr:Hilary_Putnam dbr:Wellfounded dbr:Matiyasevich's_theorem dbr:Solomon_Feferman dbr:Juliette_Kennedy dbr:Entscheidungsproblem dbr:Euclidean_geometry dbr:Isabelle_theorem_prover dbr:Kolmogorov_complexity dbr:Parallel_postulate dbr:Tractatus_Logico-Philosophicus dbr:Per_Lindström dbr:Stanley_Jaki dbr:Characteristic_(algebra) dbr:Self-verifying_theories dbr:Recursion_theory dbr:Bob_Hale_(philosopher) dbr:Omega-consistent dbr:Axiom_schema_of_specification dbr:George_Boolos dbr:Halting_problem dbr:Recursively_enumerable_set dbr:Königsberg dbr:Rudy_Rucker dbr:Principia_Mathematica dbr:Recursively_inseparable_sets dbr:Naïve_set_theory dbr:Set_theory dbc:Metatheorems dbr:Ignoramus_et_ignorabimus dbr:Nqthm dbr:Lawrence_Paulson dbr:Leo_Harrington dbr:Ernest_Nagel dbr:Stephen_Cole_Kleene dbr:J.R._Lucas dbr:Kruskal's_tree_theorem dbr:Undecidable_problem dbr:Jeremy_Stangroom dbr:Jon_Barwise dbr:Roger_Penrose dbr:Cantor's_diagonal_argument dbr:Group_theory dbr:Yuri_Matiyasevich dbr:Algorithm dbr:Paraconsistent_logic dbr:Non-standard_model_of_arithmetic dbr:Liar_paradox dbr:Paul_Cohen_(mathematician) dbr:Algorithmic_information_theory dbr:Natural_number dbr:Dense_linear_order dbr:Self_reference dbr:Hilbert's_10th_problem dbr:Jean_Bricmont dbr:First-order_logic dbr:Peano_arithmetic dbr:Peano_axioms dbr:Graham_Priest dbr:Impredicativity dbr:Intended_interpretation
dbo:wikiPageExternalLink
n10:Goedel_Incompleteness.html n10:Incompleteness.html n14:ZACKGP n18:1235416274 n21:canon00-goedel.pdf n23:Godel_Widgerson_Text.pdf n25:%23AriGodThe n36: n38: n39:10.1007%2F978-1-4419-1221-3 n41: n42:0508572 n44:0505034 n49: n52:viewcontent.cgi%3Farticle=1297&context=philos_facpubs n55: n58:problems.html%23prob2 n65:Gentzen.html n68:fea-davis.pdf n69:gt.html n72:S0273-0979-1980-14832-6.pdf n79:conprf.pdf%7C n80:books%3Fid=xUapAAAAQBAJ n65:Godel.html n82:canon00-goedel.pdf n85:revue-internationale-de-philosophie-2005-4-page-513.htm n91:Gdl-Smullyan.html n94:Logik_der_Antinomien.html
owl:sameAs
dbpedia-uk:Теореми_Геделя_про_неповноту dbpedia-ar:مبرهنات_عدم_الاكتمال_لغودل wikidata:Q200787 dbpedia-fa:قضایای_ناتمامیت_گودل dbpedia-io:Godel-teorio n15:4021417-5 n16:ဂူဒယ်၏_မပြည့်စုံခြင်းသီအိုရမ်များ dbpedia-la:Theoremata_Gödel_de_imperfectione dbpedia-fi:Gödelin_epätäydellisyyslause n22:گوڈل_نامکملیت_قضیہات dbpedia-pt:Teoremas_da_incompletude_de_Gödel dbpedia-gl:Teorema_da_incompletude_de_Gödel n29:Gödelove_teoreme_nepotpunosti n30:ಗೋಡೆಲ್‌ರ_ಅಪೂರ್ಣತೆಯ_ಪ್ರಮೇಯ dbpedia-ga:Cruthú_Gödel dbpedia-et:Gödeli_mittetäielikkuse_teoreemid dbpedia-tr:Gödel'in_eksiklik_teoremi dbpedia-pl:Twierdzenia_Gödla dbpedia-hr:Gödelovi_teoremi_nepotpunosti dbpedia-es:Teoremas_de_incompletitud_de_Gödel n40:Teoremas_de_incompletitud_de_Gödel dbpedia-da:Gödels_ufuldstændighedssætning dbpedia-ka:გოდელის_არასრულობის_თეორემები n47:ਗੋਇਡਲ_ਦੀਆਂ_ਅਪੂਰਨਤਾ_ਦੀਆਂ_ਥਿਊਰਮਾਂ dbpedia-sv:Gödels_ofullständighetssatser dbpedia-ca:Teorema_d'incompletesa_de_Gödel dbpedia-sk:Gödelova_veta_o_neúplnosti n53:गाडेल_का_अपूर्णता_प्रमेय dbpedia-vi:Các_định_lý_bất_toàn_của_Gödel dbpedia-nn:Ufullstendigheitsteorema dbpedia-zh:哥德尔不完备定理 dbpedia-nl:Onvolledigheidsstellingen_van_Gödel dbpedia-th:ทฤษฎีบทความไม่บริบูรณ์ของเกอเดิล dbpedia-sr:Геделове_теореме_о_непотпуности n62:vQmN dbpedia-eo:Teoremoj_de_nekompleteco dbpedia-el:Θεωρήματα_μη_πληρότητας_του_Γκέντελ dbpedia-hu:Gödel_első_nemteljességi_tétele n67:Tiurema_d'incumplitizza_di_Gödel dbpedia-cs:Gödelovy_věty_o_neúplnosti dbpedia-ja:ゲーデルの不完全性定理 dbpedia-he:משפטי_האי-שלמות_של_גדל dbpedia-it:Teoremi_di_incompletezza_di_Gödel dbpedia-ru:Теоремы_Гёделя_о_неполноте dbpedia-simple:Gödel's_incompleteness_theorems dbpedia-no:Gödels_ufullstendighetsteoremer n84:Гёделĕн_туллимарлăх_теореми dbpedia-de:Gödelscher_Unvollständigkeitssatz dbpedia-als:Gödelscher_Unvollständigkeitssatz dbpedia-fr:Théorèmes_d'incomplétude_de_Gödel freebase:m.0dfsl dbpedia-bg:Теорема_на_Гьодел_за_непълнота dbpedia-ko:괴델의_불완전성_정리 dbpedia-id:Teorema_ketaklengkapan_Gödel
dbp:txt
yes
dbp:wikiPageUsesTemplate
dbt:Doi dbt:Main dbt:Metalogic dbt:Zbl dbt:SEP dbt:Blockquote dbt:In_Our_Time dbt:Springer dbt:Harvard_citations dbt:Colend dbt:Not_a_typo dbt:Mr dbt:Authority_control dbt:Harvtxt dbt:Harv dbt:Tmath dbt:ISBN dbt:Mathematical_logic dbt:Mvar dbt:See_also dbt:JSTOR dbt:Harvid dbt:Harvnb dbt:Harvs dbt:Full_citation_needed dbt:Anchor dbt:Short_description dbt:Resx dbt:Math dbt:Cols dbt:MR dbt:Reflist dbt:Redirect dbt:Portal dbt:Cite_book dbt:Cite_journal
dbp:first
Stewart George Avi Stephen Cole Jean Alan Dan J. Barkley Ophelia Graham Paul Hilary Jeremy
dbp:id
p/g044530
dbp:last
Benson Willard Rosser Finsler Priest Stangroom Boolos Sokal Putnam Wigderson Kleene Shapiro Bricmont
dbp:title
Gödel incompleteness theorem
dbp:year
1984 1989 1999 2002 2000 2001 2006 2004 2010 1960 1926 1936 1943
dbo:abstract
Os teoremas da incompletude de Gödel são dois teoremas da lógica matemática que estabelecem limitações inerentes a quase todos os sistemas axiomáticos, exceto aos mais triviais. Os teoremas, provados por Kurt Gödel em 1931, são importantes tanto para a lógica matemática quanto para a filosofia da matemática. Os dois resultados são amplamente, mas não universalmente, interpretados como indicações de que o programa de Hilbert para encontrar um conjunto completo e consistente de axiomas para toda a matemática é impossível, dando uma resposta negativa para o segundo problema de Hilbert. O primeiro teorema da incompletude afirma que nenhum sistema consistente de axiomas, cujos teoremas podem ser listados por um “procedimento efetivo” (e.g., um programa de computador que pode ser qualquer tipo de algoritmo), é capaz de provar todas as verdades sobre as relações dos números naturais (aritmética). Para qualquer um desses sistemas, sempre haverá afirmações sobre os números naturais que são verdadeiras, mas que não podem ser provadas dentro do sistema. O segundo teorema da incompletude, uma extensão do primeiro, mostra que tal sistema não pode demonstrar sua própria consistência. * Teorema 1: "Qualquer teoria axiomática recursivamente enumerável e capaz de expressar algumas verdades básicas de aritmética não pode ser, ao mesmo tempo, completa e consistente. Ou seja, em uma teoria consistente, sempre há proposições que não podem ser demonstradas nem verdadeiras, nem falsas". * Teorema 2: "Uma teoria, recursivamente enumerável e capaz de expressar verdades básicas da aritmética e alguns enunciados da teoria da prova, pode provar sua própria consistência se, e somente se, for inconsistente." Теорема Гёделя о неполноте и вторая теорема Гёделя — две теоремы математической логики о принципиальных ограничениях формальной арифметики и, как следствие, всякой формальной системы, в которой можно определить основные арифметические понятия: натуральные числа, 0, 1, сложение и умножение. Первая теорема утверждает, что если формальная арифметика непротиворечива, то в ней существует невыводимая и неопровержимая формула. Вторая теорема утверждает, что если формальная арифметика непротиворечива, то в ней невыводима некоторая формула, содержательно утверждающая непротиворечивость этой арифметики. Обе эти теоремы были доказаны Куртом Гёделем в 1930 году (опубликованы в 1931) и имеют непосредственное отношение ко второй проблеме из знаменитого списка Гильберта. Chruthaigh an matamaiticeoir Meiriceánach Kurt Gödel (1906-1978) i 1931 go mbíonn tairiscintí i gcónaí taobh istigh de bhrainse ar bith matamataice nach féidir a chruthú ná a bhréagnú le bunrialacha an bhrainse sin. Thaispeáin sé gur gá dul taobh amuigh den bhrainse ina leithéid de chás agus rialacha nua a leagan amach. Meastar uaidh sin nach féidir ríomhaire a dhéanamh chomh hintleachtach le daoine, de bhrí go mbionn an ríomhaire teoranta d'oiread ar leith rialacha a leagann an dearthóir amach dó, ach gur féidir le daoine coincheapanna is fírinní gan choinne a fháil amach i gcónaí. En lògica matemàtica, els teoremes d'incompletesa de Gödel són dos cèlebres teoremes demostrats per Kurt Gödel l'any 1930. Simplificant, el primer teorema afirma: En qualsevol formalització de les matemàtiques que sigui prou forta per definir el concepte de nombres naturals, es pot construir una afirmació que ni es pot demostrar ni es pot refutar dins d'aquest sistema. Aquest teorema és un dels més famosos, més enllà de les matemàtiques, però sí i un dels pitjor compresos. És un teorema de lògica formal, i com a tal és fàcil mal interpretar-lo. N'hi ha molts que semblen similars a aquest primer teorema d'incompletesa de Gödel, però que en realitat no són certs (vegeu la secció «»). El segon teorema, que es demostra formalitzant part de la demostració del primer teorema dins el mateix sistema, afirma: Cap sistema consistent es pot usar per demostrar-se a si mateix. Aquest resultat fou devastador per a l'aproximació filosòfica a les matemàtiques conegudes com el programa de formalització de Hilbert. David Hilbert proposà que la consistència dels sistemes més complexos, tals com l'anàlisi real, es podien demostrar en termes de sistemes més senzills. Finalment, la consistència de totes les matemàtiques es podria reduir a l'aritmètica bàsica. El segon teorema d'incompletesa de Gödel demostra que l'aritmètica bàsica no es pot usar per demostrar la seva pròpia consistència i, per tant, tampoc pot demostrar la consistència de cap altre sistema més fort. 在数理逻辑中,哥德尔不完备定理是库尔特·哥德尔于1931年证明并发表的两条定理。第一条定理指出: 这是形式逻辑中的定理,容易被错误表述。有许多命题听起来很像是哥德尔不完备定理,但事实上并不是。具体实例见。 把第一条定理的证明过程在体系内部形式化后,哥德尔证明了第二条定理。该定理指出: 哥德尔不完备定理破坏了希尔伯特计划的哲学企图。大卫·希尔伯特提出,像实分析那样较为复杂的体系的相容性,可以用较为简单的体系中的手段来证明。最终,全部数学的相容性都可以归结为基本算术的相容性。但哥德尔的第二条定理证明了基本算术的相容性不能在自身内部证明,因此当然就不能用来证明比它更强的系统的相容性了。 Twierdzenia Gödla – wspólna nazwa dwóch rezultatów logiki matematycznej i metamatematyki: * twierdzenie o niezupełności arytmetyki, * jego konsekwencja nazywana też twierdzeniem o niedowodliwości niesprzeczności. Oba twierdzenia zostały udowodnione w 1931 roku przez austriackiego matematyka i logika Kurta Gödla. Uważa się również, że twierdzenia te dają negatywną odpowiedź na drugi problem Hilberta, i w ten sposób mają spore znaczenie w filozofii matematyki. Oprócz rozpatrywanych w tym artykule twierdzeń, Gödel udowodnił też twierdzenie o istnieniu modelu i twierdzenie o nierozstrzygalności (patrz: teoria, struktura matematyczna). De onvolledigheidsstellingen van Gödel zijn twee stellingen over de beperkingen van formele systemen, beide bewezen door Kurt Gödel in 1931. Door deze onvolledigheidsstellingen gaf Gödel het platonisme binnen de wiskunde een nieuw elan. Στη μαθηματική λογική, τα θεωρήματα μη πληρότητας του Γκέντελ, τα οποία αποδείχτηκαν από τον Κουρτ Γκέντελ (Kurt Gödel) το 1931, αποτελούν δύο θεωρήματα που υποδεικνύουν έμφυτους περιορισμούς σε όλα τα (πλην των τετριμμένων) τυπικά συστήματα των μαθηματικών. Τα θεωρήματα είναι πολύ σημαντικά για τη φιλοσοφία των μαθηματικών. Ερμηνεύονται γενικά ως μια απόδειξη πως το να βρεθεί ένα πλήρες και συνεπές σύνολο από αξιώματα για όλα τα μαθηματικά είναι αδύνατο, δίνοντας έτσι αρνητική απάντηση στο . Gödels ofullständighetsteorem är två fundamentala teorem inom den moderna logiken. De handlar om avgörbarhet och bevisbarhet av utsagor i formella system och lades fram av Kurt Gödel 1931. Teoremen fastlägger att Hilberts andra problem, om en axiomatisering av aritmetiken, kräver ett oändligt antal axiom. Det medför att David Hilberts program, att finna ett fullständigt och konsistent, det vill säga motsägelsefritt, axiomsystem för all matematik är ogenomförbart. Gödels första ofullständighetsteorem: I varje konsistent formellt system, tillräckligt för aritmetiken, finns en sann men oavgörbar formel, det vill säga en formel, som inte kan bevisas och vars negation ej heller kan bevisas. Gödels andra ofullständighetsproblem, är en följdsats till det första teoremet: Konsistensen hos ett formellt system, tillräckligt för aritmetiken, kan inte bevisas inom systemet. Gödels första teorem är i grunden villkorligt. Det säger att, om ett formellt system S för aritmetik är konsistent, så är det möjligt att konstruera en sats G, som är sann men obevisbar i detta system. Härav följer, att om S är konsistent, så är G både sann och obevisbar. Trivialt fås då, att om S är konsistent, så är G sann. Om konsistensen av S nu skulle kunna bevisas i systemet, så skulle G ha bevisats i S och därmed skulle en kontradiktion, G och icke-G, att G är såväl bevisbar som icke bevisbar, kunna härledas. Av reductio ad absurdum-regeln följer då negationen av satsen, att S är konsistent, det vill säga att S inte är, eller kan visas vara, konsistent. Teorema ketaklengkapan Gödel (bahasa Inggris: Gödel's incompleteness theorems) adalah dua teorema logika matematika yang menetapkan batasan (limitation) inheren dari semua kecuali sistem aksiomatik yang paling trivial yang mampu mengerjakan aritmetika. Teorema-teorema ini, dibuktikan oleh Kurt Gödel pada tahun 1931, penting baik dalam logika matematika maupun dalam filsafat matematika. Kedua hasil ini secara luas, tetapi tidak secara universal, ditafsirkan telah menunjukkan bahwa program Hilbert untuk menghitung himpunan lengkap dan konsisten dari aksioma-aksioma bagi semua matematika adalah tidak mungkin, sehingga memberikan jawaban negatif terhadap soal Hilbert yang kedua. ゲーデルの不完全性定理(ゲーデルのふかんぜんせいていり、英: Gödel's incompleteness theorems、独: Gödelscher Unvollständigkeitssatz)または不完全性定理とは、数学基礎論とコンピュータ科学(計算機科学)の重要な基本定理。(数学基礎論は数理論理学や超数学とほぼ同義な分野で、コンピュータ科学と密接に関連している。) 不完全性定理は厳密には「数学」そのものについての定理ではなく、「形式化された数学」についての定理である。クルト・ゲーデルが1931年の論文で証明した定理であり、有限の立場(形式主義)では自然数論の無矛盾性の証明が成立しないことを示す。なお、少し拡張された有限の立場では、自然数論の無矛盾性の証明が成立する()。 数学基礎論研究者の菊池誠によると不完全性定理は、20世紀初め以降に哲学から決別した数学基礎論の中で現れた。コンピュータ科学者・数理論理学者のトルケル・フランセーンおよび数学者・数理論理学者の田中一之によると、不完全性定理が示した不完全性とは、数学用語の意味での「特定の形式体系Pにおいて決定不能な命題の存在」であり、一般的な意味での「不完全性」とは無関係である。不完全性定理を踏まえても、数学の形式体系の公理は真であり無矛盾であるし、数学の完全性も成立し続けている。しかし“不完全性定理は数学や理論の「不完全性」を証明した”といった誤解や、“数学には「不完全」な部分があると証明済みであり、数学以外の分野に「不完全」な部分があってもおかしくない”といった誤解が一般社会・哲学・宗教・神学等によって広まり、誤用されている。 「」および「ゲーデルの完全性定理」も参照 数学の「無矛盾性」を証明することを目指したヒルベルト・プログラムに関して「不完全性定理がヒルベルトのプログラムを破壊した」という類の哲学的発言はよくあるが、これは実際の不完全性定理やゲーデルの見解とは異なる、とフランセーン達は解説している。正確には、ゲーデルはヒルベルトと同様の見解を持っており、彼が不完全性定理を証明して示したのは、ヒルベルトの目的(「無矛盾性証明」)を実現するためには手段(ヒルベルト・プログラム)を拡張する必要がある、ということだった。日本数学会が言うには「彼〔ゲーデル〕の結果はヒルベルトの企図を直接否定するものではなく,実際この定理の発見後に無矛盾性証明のための様々な方法論が開発されている」。 「」および「不完全性定理によるヒルベルト・プログラムの発展」も参照 مبرهنات عدم الاكتمال لغودل هما مبرهنتان في المنطق الرياضي برهنَ عليهما كورت غودل في عام 1931. وهما نظريتان تنصّان على حدود جميع الأنظمة الشكلية في الحساب.تعتبر هاتان النظريتان مهمتين في فلسفة الرياضيات، وتستخدمان لإثبات استحالة إيجاد مجموعة كاملة من البديهيات لكل علم الرياضيات ببرنامج هيلبرت، ممَّا يعطي جواباً سلبياً -بالتالي- . Gödelovy věty o neúplnosti jsou dvě důležité matematické věty, které mají zcela výsadní postavení v celé moderní matematické logice. Důležitou roli však hrají v celé matematice, zejména pak v teorii modelů, aritmetice (respektive teorii čísel) a v teorii množin. Dokázal je roku 1931 rakouský logik Kurt Gödel. Gödelovy věty jsou velmi významné i z hlediska filosofie matematiky, stanovují totiž hranice axiomatické metody v matematice. Plyne z nich například neproveditelnost takzvaného Hilbertova programu, který si kladl za cíl vytvořit bezespornou, úplnou teorii, s efektivně zadatelnou množinou axiomů, v níž by bylo možné interpretovat aritmetiku přirozených čísel. La teoremoj de nekompleteco estas du teoremoj de matematika logiko pruvitaj de Kurt Gödel en 1930. Iomete simpligite, la unua teoremo asertas: En iu ajn de matematiko, en kiu eblas difini la aritmetikon de la naturaj nombroj, eblas konstrui propozicion, kiun oni povas nek pruvi nek malpruvi. La dua teoremo, kiun oni povas derivi el la unua, asertas: En iu ajn nekontraŭdira sistemo, en kiu eblas difini la aritmetikon de la naturaj nombroj, oni ne povas pruvi la nekontraŭdirecon de tiu sistemo mem. Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency. Employing a diagonal argument, Gödel's incompleteness theorems were the first of several closely related theorems on the limitations of formal systems. They were followed by Tarski's undefinability theorem on the formal undefinability of truth, Church's proof that Hilbert's Entscheidungsproblem is unsolvable, and Turing's theorem that there is no algorithm to solve the halting problem. In logica matematica, i teoremi di incompletezza di Gödel sono due famosi teoremi dimostrati da Kurt Gödel nel 1930. Gödel annunciò il suo primo teorema di incompletezza in una tavola rotonda a margine della Seconda Conferenza sull'Epistemologia delle Scienze esatte di Königsberg. John von Neumann, presente alla discussione, riuscì a dimostrare il teorema per conto suo verso la fine del 1930 e, inoltre, fornì una dimostrazione del secondo teorema di incompletezza, che annunciò a Gödel in una lettera datata 20 novembre 1930. Gödel aveva, nel frattempo, a sua volta ottenuto una dimostrazione del secondo teorema di incompletezza, e lo incluse nel manoscritto che fu ricevuto dalla rivista Monatshefte für Mathematik il 17 novembre 1930. Essi fanno parte dei teoremi limitativi, che precisano le proprietà che i sistemi formali non possono avere. 괴델의 불완전성 정리(영어: Gödel’s incompleteness theorems)는 수리논리학에서 페아노 공리계를 포함하는 모든 무모순적 공리계는 참인 일부 명제를 증명할 수 없으며, 특히 스스로의 무모순성을 증명할 수 없다는 정리다. Los teoremas de incompletitud de Gödel son dos célebres teoremas de lógica matemática demostrados por Kurt Gödel en 1931. Ambos están relacionados con la existencia de proposiciones indecidibles en ciertas teorías aritméticas. Les théorèmes d'incomplétude de Gödel sont deux théorèmes célèbres de logique mathématique, publiés par Kurt Gödel en 1931 dans son article (en) (« Sur les propositions formellement indécidables des Principia Mathematica et des systèmes apparentés »). Ils ont marqué un tournant dans l'histoire de la logique en apportant une réponse négative à la question de la démonstration de la cohérence des mathématiques posée plus de 20 ans auparavant par le programme de Hilbert. Le premier théorème d'incomplétude établit qu'une théorie cohérente suffisante pour y démontrer les théorèmes de base de l'arithmétique est nécessairement incomplète, au sens où il existe des énoncés qui n'y sont ni démontrables, ni réfutables (un énoncé est démontrable si on peut le déduire des axiomes de la théorie, il est réfutable si on peut déduire sa négation). On parle alors d'énoncés indécidables dans la théorie. Le second théorème d'incomplétude est à la fois un corollaire et une formalisation d'une partie de la preuve du premier. Il traite le problème des preuves de cohérence d'une théorie : une théorie est cohérente s'il existe des énoncés qui n'y sont pas démontrables (ou, ce qui revient au même, si on ne peut y démontrer A et non A) ; par exemple on exprime souvent la cohérence de l'arithmétique par le fait que l'énoncé 0 = 1 n'y est pas démontrable (sachant que bien entendu 0 ≠ 1 l'est). Sous des hypothèses à peine plus fortes que celles du premier théorème, on peut construire un énoncé exprimant la cohérence d'une théorie dans le langage de celle-ci. Le second théorème affirme alors que si la théorie est cohérente cet énoncé ne peut pas en être conséquence, ce que l'on peut résumer par : « une théorie cohérente ne démontre pas sa propre cohérence ». Теорема Геделя про неповноту і друга теорема Геделя (англ. Gödel's incompleteness theorems) — дві теореми математичної логіки про принципові обмеження формальної арифметики і, як наслідок, будь-якої формальної системи, в якій можливо визначити основні арифметичні поняття: натуральні числа, 0, 1, додавання та множення. Перша теорема стверджує, що, якщо формальна арифметика є несуперечливою, то в ній існує невивідна і неспростовна формула. Друга теорема стверджує, що якщо формальна арифметика є несуперечливою, то в ній є невивідною деяка формула, яка змістовно стверджує несуперечливість цієї арифметики. Обидві ці теореми було доведено Куртом Геделем 1930 року (опубліковано 1931 року), вони мають безпосередній стосунок до зі знаменитого списку Гільберта. Der Gödelsche Unvollständigkeitssatz ist einer der wichtigsten Sätze der modernen Logik. Er beschäftigt sich mit der Ableitbarkeit von Aussagen in formalen Systemen. Der Satz zeigt die Grenzen der formalen Systeme ab einer bestimmten Leistungsfähigkeit auf. Er weist nach, dass es in hinreichend starken Systemen, wie der Arithmetik, Aussagen geben muss, die man formal weder beweisen noch widerlegen kann. Der Satz beweist damit die Undurchführbarkeit des Hilbertprogramms, das von David Hilbert unter anderem begründet wurde, um die Widerspruchsfreiheit der Mathematik zu beweisen. Der Satz wurde 1931 von dem österreichischen Mathematiker Kurt Gödel veröffentlicht. Genauer werden zwei Unvollständigkeitssätze unterschieden: Der erste Unvollständigkeitssatz besagt, dass es in allen hinreichend starken widerspruchsfreien Systemen unbeweisbare Aussagen gibt. Der zweite Unvollständigkeitssatz besagt, dass hinreichend starke widerspruchsfreie Systeme ihre eigene Widerspruchsfreiheit nicht beweisen können. Durch diese Sätze ist der Mathematik eine prinzipielle Grenze gesetzt: Nicht jeder mathematische Satz kann aus den Axiomen eines mathematischen Teilgebietes (zum Beispiel Arithmetik, Geometrie und Algebra) formal abgeleitet oder widerlegt werden. In der Wissenschaftstheorie und anderen Gebieten der Philosophie zählt der Satz zu den meistrezipierten der Mathematik. Das Buch Gödel, Escher, Bach und die Werke von John Randolph Lucas werden häufig exemplarisch hervorgehoben.
dbp:author1Link
Avi Wigderson Stephen Cole Kleene Dan Willard Ophelia Benson J. Barkley Rosser Hilary Putnam Alan Sokal Stewart Shapiro Paul Finsler George Boolos Graham Priest
dbp:author2Link
Jeremy Stangroom Jean Bricmont
gold:hypernym
dbr:Theorems
prov:wasDerivedFrom
wikipedia-en:Gödel's_incompleteness_theorems?oldid=1124610774&ns=0
dbo:wikiPageLength
89645
foaf:isPrimaryTopicOf
wikipedia-en:Gödel's_incompleteness_theorems
Subject Item
dbr:Hans-Werner_Bothe
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Hilbert's_problems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Hilbert_space
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Chinese_remainder_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:John_Boyd_(military_strategist)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:John_Lucas_(philosopher)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Lambda_calculus
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:System
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Heyting_arithmetic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Theory_of_everything_(philosophy)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Torkel_Franzén
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Zeno's_paradoxes
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Remarks_on_the_Foundations_of_Mathematics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:The_Ancient_Tradition_of_Geometric_Problems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Douglas_Hofstadter
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Axiom_of_infinity
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Axiomatic_system
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Martin_Goldstern
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Positivism
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_Incompleteness_Theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_diagonalization_method
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_incompleteness_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_diagonalization_method
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_first_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_incompleteness_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_proof
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_second_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel_first_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel_incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel_proof
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel_second_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel_sentence
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goerdel's_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_first_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_proof
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:War_against_war
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gōdel's_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gōdel's_Incompleteness_Theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Kurt_Gödel
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbp:knownFor
dbr:Gödel's_incompleteness_theorems
dbo:knownFor
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Cantor's_diagonal_argument
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Raymond_Smullyan
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Certainty
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Second_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Self-reference
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Set_(mathematics)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Set_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Sequent_calculus
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Incomplete
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageDisambiguates
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Loop_variant
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Mechanism_(philosophy)
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Von_Neumann_universe
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Usenet_personality
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Euclidean_geometry
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Extensions_of_First_Order_Logic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Diagonal_argument
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:I_Am_a_Strange_Loop
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Playing_with_Infinity
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Natalie_Wolchover
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:The_Difference_Engine
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Weimar_culture
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Rosser's_trick
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Ordinal_logic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Relationship_between_mathematics_and_physics
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Semantic_theory_of_truth
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Ω-consistent_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Philosophy_of_logic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Tarski's_undefinability_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Rice's_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Sheri_Markose
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Kurt_Gödel's_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Incompleteness_of_formalized_arithmetic
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_First_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_Incompleteness_Theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_diagonalization_method
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_incompleteness_theory
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_second_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel's_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel_first_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel_incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel_second_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel_sentence
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödels_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Gödel’s_incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_Undecidability_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_consistency_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_first_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel's_second_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel-Rosser_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_first_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_incompleteness
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_incompleteness_theorm
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_second_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_sentence
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godels_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel’s_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Godel’s_incompleteness_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedel's_theorems
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedels_Incompleteness_Theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Goedels_incompleteness_theorem
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
dbr:Theorem_of_Incompleteness
dbo:wikiPageWikiLink
dbr:Gödel's_incompleteness_theorems
dbo:wikiPageRedirects
dbr:Gödel's_incompleteness_theorems
Subject Item
wikipedia-en:Gödel's_incompleteness_theorems
foaf:primaryTopic
dbr:Gödel's_incompleteness_theorems