The Consistency of $ZFC+CIFS$

Details The Consistency of $ZFC+CIFS$ The Consistency of $ZFC+CIFS$

1993-04-15

arxiv.org/abs/math/9304203v1

Mathematics

Logic

Scientific paper

This paper is a technical continuation of ``Natural Axiom Schemata Extending ZFC. Truth in the Universe?'' In that paper we argue that $CIFS$ is a natural axiom schema for the universe of sets. In particular it is a natural closure condition on $V$ and a natural generalization of $IFS(L).$ Here we shall prove the consistency of $ZFC\ +\ CIFS$ relative to the existence of a transitive model of $ZFC$ using the compactness theorem together with a class forcing.

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