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On countable cofinality and decomposition of definable thin orderings

Volume 235 / 2016

Vladimir Kanovei, Vassily Lyubetsky Fundamenta Mathematicae 235 (2016), 13-36 MSC: Primary 03E15; Secondary 03E35. DOI: 10.4064/fm977-10-2015 Published online: 11 May 2016

Abstract

We prove that in some cases definable thin sets (including chains) of Borel partial orderings are necessarily countably cofinal. This includes the following cases: analytic thin sets, ROD thin sets in the Solovay model, and ${\mathbf \Sigma }_{2}^{1}$ thin sets under the assumption that $\omega _{1}^{{\bf L}[x]} \lt \omega _{1}$ for all reals $x$. We also prove that definable thin wellorderings admit partitions into definable chains in the Solovay model.

Authors

  • Vladimir KanoveiIITP RAS and MIIT
    Moscow, Russia
    e-mail
  • Vassily LyubetskyIITP RAS
    Moscow, Russia
    e-mail

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