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- Title
THE ${\bf{\Sigma }}_2^1$ COUNTERPARTS TO STATEMENTS THAT ARE EQUIVALENT TO THE CONTINUUM HYPOTHESIS.
- Authors
TÖRNQUIST, ASGER; WEISS, WILLIAM
- Abstract
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.
- Subjects
CONTINUUM hypothesis; DESCRIPTIVE set theory; MATHEMATICAL proofs; PARTITION functions; DEFINABILITY theory (Mathematical logic)
- Publication
Journal of Symbolic Logic, 2015, Vol 80, Issue 4, p1075
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2014.20