On initial segments of degrees of constructibility |
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Authors: | V G Kanovei |
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Institution: | 1. M. V. Lomonosov Moscow State University, USSR
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Abstract: | Let \(\mathfrak{M}\) be a fixed countable standard transitive model of ZF+V=L. We consider the structure Mod of degrees of constructibility of real numbers x with respect to \(\mathfrak{M}\) such that \(\mathfrak{M}\) (x) is a model. An initial segment Q \( \subseteq \) Mod is called realizable if some extension of \(\mathfrak{M}\) with the same ordinals contains exclusively the degrees of constructibility of real numbers from Q (and is a model of Z FC). We prove the following: if Q is a realizable initial segment, then $$y \in Q \to y< x]]\& \forall z\exists yz< x \to y \in Q\& \sim y< z]]]$$ . |
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