%0 Journal Article
%T On countable cofinality and decomposition of definable thin orderings
%A Vladimir Kanovei
%A Vassily Lyubetsky
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1412.0195v1