About: Equiconsistency

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In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa. In this case, they are, roughly speaking, "as consistent as each other".

Attributes	Values
rdfs:label	Equiconsistency (en)
rdfs:comment	In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa. In this case, they are, roughly speaking, "as consistent as each other". (en)
sameAs	Equiconsistency Equiconsistency
dbp:wikiPageUsesTemplate	dbt:ISBN dbt:Reflist dbt:Short_description dbt:Var dbt:Metalogic
Subject	Large cardinals Mathematical logic
gold:hypernym	Equiconsistent
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Equiconsistency?oldid=1018408106&ns=0
Wikipage page ID	3435716 (xsd:integer)
page length (characters) of wiki page	5258 (xsd:nonNegativeInteger)
Wikipage revision ID	1018408106 (xsd:integer)
Link from a Wikipage to another Wikipage	Forcing (mathematics) Mahlo cardinal Akihiro Kanamori Arithmetic Aronszajn tree Axiom of determinacy Large cardinals Mathematical logic David Hilbert Kurepa tree Kurt Gödel Metamathematics Second-order arithmetic Set theory Zermelo–Fraenkel set theory List of Latin phrases (V) Primitive recursive arithmetic Robinson arithmetic Computably enumerable Consistency Continuum hypothesis Hilbert's program Reverse mathematics Inaccessible cardinal Gödel's incompleteness theorems Peano axioms Weakly compact cardinal Theory (mathematical logic) The Higher Infinite Large cardinal Mathematical logic Mathematical object
has abstract	In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa. In this case, they are, roughly speaking, "as consistent as each other". In general, it is not possible to prove the absolute consistency of a theory T. Instead we usually take a theory S, believed to be consistent, and try to prove the weaker statement that if S is consistent then T must also be consistent—if we can do this we say that T is consistent relative to S. If S is also consistent relative to T then we say that S and T are equiconsistent. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Equiconsistency
is Wikipage redirect of	Equiconsistent Consistency strength
is Link from a Wikipage to another Wikipage of	Foundations of geometry Non-Euclidean geometry Axiom of constructibility Azriel Lévy Beltrami–Klein model Church's thesis (constructive mathematics) Lisl Gaal List of large cardinal properties Consistency Consistency (disambiguation) Hilbert's second problem Moti Gitik Elementary sentence Elementary theory First-order logic Ineffable cardinal Inner model Inner model theory Kripke–Platek set theory Eugenio Beltrami Large cardinal Measurable cardinal History of numbers New Foundations Equiconsistent Consistency strength
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Equiconsistency

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