About: Non-well-founded set theory

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Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation.

Attributes	Values
rdf:type	mean of transportation yago:Artifact100021939 yago:Instrumentality103575240 yago:Object100002684 yago:PhysicalEntity100001930 yago:System104377057 yago:Whole100003553 yago:WikicatSystemsOfSetTheory
rdfs:label	Théorie des ensembles non bien fondés (fr) Non-well-founded set theory (en) Hiperconjunto (pt)
rdfs:comment	Em ZFC sem o axioma da regularidade, a possibilidade de infundados conjuntos surgem. Estes conjuntos, se existem, são também chamados hiperconjuntos. Claramente, se A ∈ A, então A é um hiperconjunto. Em 1988, Peter Aczel publicou um trabalho influente, Non-Well-Founded Sets (Conjuntos Não-Bem-Fundados). A teoria dos hiperconjuntos tem sido aplicada à ciência computacional (processamento algébrico e semântica limite), linguística (teoria da situação), e filosofia (trabalho sobre o paradoxo de Liar). (pt) Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. (en) La théorie des ensembles non bien fondés est une variante de la théorie axiomatique des ensembles qui permet aux ensembles de s'appartenir les uns aux autres sans limite. Autrement dit, c'est une théorie des ensembles qui ne satisfait pas l'axiome de fondation. Plus précisément, dans la théorie des ensembles non bien fondés, l'axiome de fondation de ZFC est remplacé par un axiome impliquant sa négation. (fr)
dcterms:subject	Systems of set theory Wellfoundedness Self-reference
Wikipage page ID	1091767 (xsd:integer)
Wikipage revision ID	1108319949 (xsd:integer)
Link from a Wikipage to another Wikipage	New Foundations Binary relation John von Neumann Paul Bernays Peter Aczel Independence (mathematical logic) Anti-Foundation Axiom Ernst Specker Liar's paradox Liar Paradox Logic Computing Axiomatic set theory Aczel's anti-foundation axiom Turtles all the way down Well-foundedness Willard Van Orman Quine Dmitry Mirimanoff John Etchemendy Jon Barwise Linguistics Situation theory Dana Scott Alternative set theory Accessible pointed graph Non-standard analysis Nonstandard analysis Systems of set theory Bisimulation ZFC Wellfoundedness Self-reference Axiom Axiom of extensionality Axiom of regularity Habilitationsschrift Metamath Semantics Von Neumann universe Universal set Extensionality Natural language Paul Finsler dbr:Maurice_Boffa Well-founded set Quine atom Process algebra Model (abstract) dbr:Final_semantics dbr:Hyperset_theory dbr:Rieger's_theorem dbr:Superuniversality
Link from a Wikipage to an external page	http://www1.maths.leeds.ac.uk/~rathjen/russelle.pdf http://repository.bilkent.edu.tr/bitstream/11693/25955/1/Issues%20in%20commonsense%20set%20theory.pdf http://us.metamath.org/mpegif/ax-reg.html http://tinf2.vub.ac.be/~dvermeir/mirrors/www.cs.bilkent.edu.tr/%257Eakman/jour-papers/air/node8.html https://archive.org/details/nonwellfoundedse0000acze/page/ https://books.google.com/books%3Fid=L3M8DwAAQBAJ https://books.google.com/books%3Fid=TM3AKPYdQVgC https://books.google.com/books%3Fid=TM3AKPYdQVgC&pg=PA186 https://books.google.com/books%3Fid=zbGjAQAAQBAJ http://plato.stanford.edu/entries/nonwellfounded-set-theory/ http://users.auth.gr/~tzouvara/Texfiles.htm/non-well.pdf%7Cyear=2003
sameAs	Non-well-founded set theory Non-well-founded set theory Non-well-founded set theory Non-well-founded set theory Non-well-founded set theory Non-well-founded set theory Non-well-founded set theory
dbp:wikiPageUsesTemplate	dbt:Set_theory dbt:Citation dbt:Cite_book dbt:Cite_web dbt:Expand_section dbt:Reflist dbt:Sfnp dbt:Short_description dbt:Mathematical_logic
has abstract	Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. The study of non-well-founded sets was initiated by Dmitry Mirimanoff in a series of papers between 1917 and 1920, in which he formulated the distinction between well-founded and non-well-founded sets; he did not regard well-foundedness as an axiom. Although a number of axiomatic systems of non-well-founded sets were proposed afterwards, they did not find much in the way of applications until Peter Aczel’s in 1988.The theory of non-well-founded sets has been applied in the logical modelling of non-terminating computational processes in computer science (process algebra and ), linguistics and natural language semantics (situation theory), philosophy (work on the Liar Paradox), and in a different setting, non-standard analysis. (en) La théorie des ensembles non bien fondés est une variante de la théorie axiomatique des ensembles qui permet aux ensembles de s'appartenir les uns aux autres sans limite. Autrement dit, c'est une théorie des ensembles qui ne satisfait pas l'axiome de fondation. Plus précisément, dans la théorie des ensembles non bien fondés, l'axiome de fondation de ZFC est remplacé par un axiome impliquant sa négation. L'étude des ensembles non-bien-fondés a été initiée par Demetrius Mirimanoffdans une série d'articles qu'il a publié en français entre 1917 et 1920 et dans lesquels il énonce une distinction entre des suites bien fondées et des suites non bien fondées ; cependant il ne fait pas recours à un axiome de bonne fondation. Alors que plusieurs axiomatiques pour les ensembles non bien fondés ont été proposées par la suite, aucune n'a trouvé d'application jusqu'à ce que Peter Aczel propose sa théorie des hyper-ensembles en 1988. La théorie des ensembles non-bien-fondés permet d'offrir des modèles pour la non-terminaison des calculs de processus en informatique (algèbre de processus), pour la linguistique et pour la sémantique du langage naturel. De plus elle a des applications en philosophie (paradoxe du menteur ) et en analyse non standard. (fr)

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