On countable cofinality and decomposition of definable thin orderings

• Autorzy: Vladimir Kanovei , Vassily Lyubetsky
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E15: Descriptive set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 235
• Numer: 1
• Strony: 13-36

Daty

wydano

2016

Twórcy

autor

Vladimir Kanovei

• IITP RAS and MIIT, Moscow, Russia

autor

Vassily Lyubetsky

• IITP RAS, Moscow, Russia

Identyfikatory

DOI

10.4064/fm977-10-2015