Geodesic
On countable cofinality and decomposition of definable thin orderings
Vladimir Kanovei1 ; Vassily Lyubetsky2
1 IITP RAS and MIIT Moscow, Russia
2 IITP RAS Moscow, Russia
Fundamenta Mathematicae, Tome 235 (2016) no. 1, pp. 13-36 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 ${\mathbf \Sigma }_{2}^{1}$ 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.
DOI : 10.4064/fm977-10-2015
Keywords: prove cases definable thin sets including chains borel partial orderings necessarily countably cofinal includes following cases analytic thin sets rod thin sets solovay model mathbf sigma thin sets under assumption omega omega reals nbsp prove definable thin wellorderings admit partitions definable chains solovay model

Vladimir Kanovei 1 ; Vassily Lyubetsky 2

1 IITP RAS and MIIT Moscow, Russia
2 IITP RAS Moscow, Russia 
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Vladimir Kanovei; Vassily Lyubetsky. On countable cofinality and decomposition of definable thin orderings. Fundamenta Mathematicae, Tome 235 (2016) no. 1, pp. 13-36. doi: 10.4064/fm977-10-2015

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