On countable cofinality and decomposition of definable thin orderings

arxiv: 1412.0195 · v1 · pith:I7IIUCSUnew · submitted 2014-11-30 · 🧮 math.LO

On countable cofinality and decomposition of definable thin orderings

Vladimir Kanovei , Vassily Lyubetsky This is my paper

classification 🧮 math.LO

keywords thindefinablesetscaseschainsmodelomegaorderings

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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 $\Sigma^1_2$ thin sets in the assumption that $\omega_1^{L[x]}<\omega_1$ for all reals $x$. We also prove that definable thin wellorderings admit partitions into definable chains in the Solovay model.

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On countable cofinality and decomposition of definable thin orderings

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