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This article is cited in 1 scientific paper (total in 1 paper)
On initial segments of degrees of constructibility
V. G. Kanovei M. V. Lomonosov Moscow State University
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 $Q\subseteq\operatorname{Mod}$ 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 $ZFC$). We prove the following: if $Q$ is a realizable initial segment, then $\exists\,x\ [\forall\,y\ [x\in\operatorname{Mod}\&[y\in Q\to y<x]]\&\forall\,z\ \exists\,y\ [z<x\to y\in Q\&\ {\sim}[y<z]]]$.
Received: 15.01.1974
Citation:
V. G. Kanovei, “On initial segments of degrees of constructibility”, Mat. Zametki, 17:6 (1975), 939–946; Math. Notes, 17:6 (1975), 563–567
Linking options:
https://www.mathnet.ru/eng/mzm7614 https://www.mathnet.ru/eng/mzm/v17/i6/p939
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