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arXiv · 1312.2064

On countable cofinality of definable chains in Borel partial orders

Vladimir Kanovei
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Abstract

We prove that in some cases definable chains of Borel partial orderings are necessarily countably cofinal. This includes the following cases: analytic chains, ROD chains in the Solovay model, and $\Sigma^1_2$ chains in the assumption that $\omega_1^{L[x]}<\omega_1$ for all reals $x$.

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Vladimir Kanovei. 2013-12-07. On countable cofinality of definable chains in Borel partial orders. https://doi.org/10.4064/fm977-10-2015

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