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A Proof of the Relative Consistency of
Concrete Models of Set Theory
12 other sections not shown
a-recursive admissible ordinal arguments arithmetic assume automorphism axiom of choice bounded cardinal closure computation condition consistent constructible sets continuum hypothesis Corollary countable D-prod deduction definition degree denote domain elementary extension elementary submodel elements embedding end extension equations equivalent exists finite sets formula free variables function symbols functor given Godel Hence holds I0-formula induction infinite inner model isomorphism Keisler Kleene language lattice lemma logic M-definable mapping Math metafinite metarecursion theory metarecursively enumerable set minimal model of ZF natural numbers notation notion obtained order type ordered set partial function partial recursive polyadic algebra predicate primitive recursive primitive recursive function proof properties proposition provable proved quantifiers recursion theory recursive function recursive ordinals regressive isols relation relativized replaced replicas restricted result satisfies saturated models schema sentences sequence set theory Skolem functions Suppose theorem transfinite ultrafilter ultrapower ultraproduct