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arXiv · 1705.02975

Definable ${\mathsf E}_0$ classes at arbitrary projective levels

Vladimir Kanovei·Vassily Lyubetsky
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Abstract

Using a modification of the invariant Jensen forcing, we define a model of ZFC, in which, for a given $n\ge3$, there exists a lightface $\varPi^1_n$ set of reals, which is a ${\mathsf E}_0$ equivalence class, hence a countable set, and which does not contain any OD element, while every non-empty countable $\varSigma^1_n$ set of reals is necessarily constructible, hence contains only OD reals.

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BibTeXRIS

Vladimir Kanovei, Vassily Lyubetsky. 2017-05-08. Definable ${\mathsf E}_0$ classes at arbitrary projective levels. https://doi.org/10.1016/j.apal.2018.04.006

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