The \mathbfΣ¹₂ counterparts to statements that are equivalent to the Continuum Hypothesis

2012/01/01 by Asger Törnquist, Asger Tornquist, Jason Weiss +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Mathematical and Theoretical Analysis #math.LO #msc:03E15 #msc:03E45 #msc:03E50

paper · pdf · doi:10.48550/arxiv.1201.0382

Several minor corrections throughout. Finally submitted

arxiv created 2012/11/26 · arxiv updated 2012/11/27

Abstract

We consider natural Σ¹₂ definable analogues of many of the classical statements that have been shown to be equivalent to CH. It is shown that these Σ¹₂ analogues are equivalent to that all reals are constructible. We also prove two partition relations for Σ¹₂ colourings which hold precisely when there is a non-constructible real.

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