Indiscernible pairs of countable sets of reals at a given projective   level

Vladimir Kanovei; Vassily Lyubetsky

arXiv:1912.12962·math.LO·January 1, 2020

Indiscernible pairs of countable sets of reals at a given projective level

Vladimir Kanovei, Vassily Lyubetsky

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Abstract

Using an invariant modification of Jensen's "minimal $Π_{2}^{1}$ singleton" forcing, we define a model of ZFC, in which, for a given $n \geq 2$ , there exists a lightface $Π_{n}^{1}$ unordered pair of non-OD (hence, OD-indiscernible) countable sets of reals, but there is no $Σ_{n}^{1}$ unordered pairs of this kind.

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TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras