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Summary Of: ZFC
ZFC consists of a single primitive... ZFC is a one... The axioms of ZFC govern how sets behave and interact... All formulations of ZFC imply that at least one set exists... be any formula in the language of ZFC with free variables among... it is impossible to axiomatize ZFC using only finitely many axioms... NBG and ZFC are equivalent set theories in the sense that any... of ZFC cannot be proved within ZFC itself... to the extent that ZFC is identified with ordinary mathematics... the consistency of ZFC cannot be demonstrated in ordinary mathematics... The consistency of ZFC does follow from the existence of a weakly... which is unprovable in ZFC if ZFC is consistent... it is unlikely that ZFC harbors an unsuspected contradiction... ZFC is immune to the classic paradoxes of... of ZFC without the axiom of regularity... One piece of evidence bearing on ZFC as a foundation of mathematics is... ZFC does not prove the existence of the... Some statements independent of ZFC can be proven to hold in particular... Since ZFC satisfies the conditions of G... the consistency of ZFC is unprovable in ZFC... ZFC has been criticized both for being excessively strong and for being excessively weak... ZFC is comparatively weak... ZFC does not admit the existence of a... of sets under ZFC is not closed under the elementary operations of the... ZFC does not admit the existence of... but critics argue these restrictions make the ZFC axioms fail to capture the informal concept of... A further comparative weakness of ZFC is that the... included in ZFC is weaker than the... AD to be established in ZFC adjoined by some large cardinal axiom... instead of ZFC so that proofs involving... Encyclodia Page On: ZFC
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