Godel’s constructibility was generalized, in a natural way, by Levy and Shoenfield to a relative constructibility which assures us of the existence of a standard transitive model L[a] of ZF for each set a. Levy-Shoenfield’s relative constructibility is rather narrow but quite easily generalized. Ln this section we will study a general theory of relative constructibility and deal with several basic relative constructibilities as special cases. Later we will extend our relative constructibility to Boolean valued relative constructibility from which we will in turn define forcing.
KeywordsFree Variable Transitive Closure Predicate Symbol Relative Constructibility Axiom Schema
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