This HTML5 document contains 35 embedded RDF statements represented using HTML+Microdata notation.

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

Namespace Prefixes

Prefix	IRI
dcterms	http://purl.org/dc/terms/
dbo	http://dbpedia.org/ontology/
foaf	http://xmlns.com/foaf/0.1/
n14	https://global.dbpedia.org/id/
dbt	http://dbpedia.org/resource/Template:
rdfs	http://www.w3.org/2000/01/rdf-schema#
rdf	http://www.w3.org/1999/02/22-rdf-syntax-ns#
owl	http://www.w3.org/2002/07/owl#
wikipedia-en	http://en.wikipedia.org/wiki/
dbp	http://dbpedia.org/property/
dbc	http://dbpedia.org/resource/Category:
prov	http://www.w3.org/ns/prov#
xsdh	http://www.w3.org/2001/XMLSchema#
wikidata	http://www.wikidata.org/entity/
dbr	http://dbpedia.org/resource/

Statements

Subject Item

dbr:Conservativity_theorem

dbo:wikiPageWikiLink

dbr:Extension_by_new_constant_and_function_names

dbo:wikiPageRedirects

dbr:Extension_by_new_constant_and_function_names

Subject Item

dbr:Conservative_extension

dbo:wikiPageWikiLink

dbr:Extension_by_new_constant_and_function_names

Subject Item

dbr:Extension_by_definitions

dbo:wikiPageWikiLink

dbr:Extension_by_new_constant_and_function_names

Subject Item

dbr:Extension_by_new_constant_and_function_names

rdfs:label

Extension by new constant and function names

rdfs:comment

In mathematical logic, a theory can be extended withnew constants or function names under certain conditions with assurance that the extension will introduceno contradiction. Extension by definitions is perhaps the best-known approach, but it requiresunique existence of an object with the desired property. Addition of new names can also be donesafely without uniqueness. Suppose that a closed formula is a theorem of a first-order theory . Let be a theory obtained from by extending its language with new constants and adding a new axiom .

dcterms:subject

dbc:Proof_theory dbc:Mathematical_logic dbc:Theorems_in_the_foundations_of_mathematics

dbo:wikiPageID

2101754

dbo:wikiPageRevisionID

1065890419

dbo:wikiPageWikiLink

dbr:Mathematical_logic dbc:Theorems_in_the_foundations_of_mathematics dbc:Mathematical_logic dbr:Extension_by_definition dbr:Functional_predicate dbr:Conservative_extension dbr:Formal_language dbr:Axiom dbr:Theory_(mathematical_logic) dbc:Proof_theory dbr:First-order_theory dbr:Extension_by_definitions

owl:sameAs

wikidata:Q5163116 n14:4iPBh

dbp:wikiPageUsesTemplate

dbt:Citation_needed dbt:Reflist dbt:Mathlogic-stub dbt:Mathematical_logic dbt:Logic-stub

dbo:abstract

In mathematical logic, a theory can be extended withnew constants or function names under certain conditions with assurance that the extension will introduceno contradiction. Extension by definitions is perhaps the best-known approach, but it requiresunique existence of an object with the desired property. Addition of new names can also be donesafely without uniqueness. Suppose that a closed formula is a theorem of a first-order theory . Let be a theory obtained from by extending its language with new constants and adding a new axiom . Then is a conservative extension of , which means that the theory has the same set of theorems in the original language (i.e., without constants ) as the theory . Such a theory can also be conservatively extended by introducing a new functional symbol: Suppose that a closed formula is a theorem of a first-order theory , where we denote . Let be a theory obtained from by extending its language with a new functional symbol (of arity ) and adding a new axiom . Then is a conservative extension of , i.e. the theories and prove the same theorems not involving the functional symbol ). Shoenfield states the theorem in the form for a new function name, and constants are the same as functionsof zero arguments. In formal systems that admit ordered tuples, extension by multiple constants as shown here can be accomplished by addition of a new constant tuple and the new constant names having the values of elements of the tuple.

prov:wasDerivedFrom

wikipedia-en:Extension_by_new_constant_and_function_names?oldid=1065890419&ns=0

dbo:wikiPageLength

2618

foaf:isPrimaryTopicOf

wikipedia-en:Extension_by_new_constant_and_function_names

Subject Item

wikipedia-en:Extension_by_new_constant_and_function_names

foaf:primaryTopic

dbr:Extension_by_new_constant_and_function_names