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THE
${\bf{\Sigma }}_2^1$ COUNTERPARTS TO STATEMENTS THAT ARE EQUIVALENT TO THE CONTINUUM HYPOTHESIS
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- Journal:
- The Journal of Symbolic Logic / Volume 80 / Issue 4 / December 2015
- Published online by Cambridge University Press:
- 22 December 2015, pp. 1075-1090
- Print publication:
- December 2015
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- Article
- Export citation
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We consider natural
${\rm{\Sigma }}_2^1$ definable analogues of many of the classical statements that have been shown to be equivalent to CH. It is shown that these 
${\rm{\Sigma }}_2^1$ analogues are equivalent to that all reals are constructible. We also prove two partition relations for 
${\rm{\Sigma }}_2^1$ colourings which hold precisely when there is a non-constructible real.
