The $ \mathbfΣ^1_2$ counterparts to statements that are equivalent to the Continuum Hypothesis

Details The $ \mathbfΣ^1_2$ counterparts to statements that are equivalent to the Continuum Hypothesis The $ \mathbfΣ^1_2$ counterparts to statements that are equivalent to the Continuum Hypothesis

2012-01-01

arxiv.org/abs/1201.0382v1

Mathematics

Logic

15 pages

Scientific paper

We consider natural $\Sigma^1_2$ definable analogues of many of the classical
statements that have been shown to be equivalent to CH. It is shown that these
$\Sigma^1_2$ analogues are equivalent to that all reals are constructible. We
also prove two partition relations for $\Sigma^1_2$ colourings which hold
precisely when there is a non-constructible real.

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