On countable cofinality and decomposition of definable thin orderings

Vladimir Kanovei, and Vassily Lyubetsky. "On countable cofinality and decomposition of definable thin orderings." Fundamenta Mathematicae 235.1 (2016): 13-36. <http://eudml.org/doc/286182>.

@article{VladimirKanovei2016,
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 Σ¹₂ thin sets under the assumption that $ω₁^\{L[x]\} < ω₁$ for all reals x. We also prove that definable thin wellorderings admit partitions into definable chains in the Solovay model.},
author = {Vladimir Kanovei, Vassily Lyubetsky},
journal = {Fundamenta Mathematicae},
keywords = {thin sets; countably cofinal; Solovay model; definable chains},
language = {eng},
number = {1},
pages = {13-36},
title = {On countable cofinality and decomposition of definable thin orderings},
url = {http://eudml.org/doc/286182},
volume = {235},
year = {2016},
}

TY - JOUR
AU - Vladimir Kanovei
AU - Vassily Lyubetsky
TI - On countable cofinality and decomposition of definable thin orderings
JO - Fundamenta Mathematicae
PY - 2016
VL - 235
IS - 1
SP - 13
EP - 36
AB - 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 Σ¹₂ thin sets under the assumption that $ω₁^{L[x]} < ω₁$ for all reals x. We also prove that definable thin wellorderings admit partitions into definable chains in the Solovay model.
LA - eng
KW - thin sets; countably cofinal; Solovay model; definable chains
UR - http://eudml.org/doc/286182
ER -