Linear ROD subsets of Borel partial orders are countably cofinal in the Solovay model

Vladimir Kanovei

doi:10.1016/j.amc.2011.05.003

Linear ROD subsets of Borel partial orders are countably cofinal in the Solovay model

Logic 2018-08-16 v2

Authors: Vladimir Kanovei

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

The following is true in the Solovay model. 1. If $\le$ is a Borel partial order on a set $D$ of the reals, and $X$ is a ROD subset of $D$ linearly ordered by $\le$ , then the restriction of $\le$ onto $X$ is countably cofinal. 2. If in addition every countable set $Y$ of $D$ has a strict upper bound in the sense of $\le$ then the ordering $< D ; \le >$ has no maximal chains that are ROD sets.

Keywords

Solovay model Borel partial order ROD subset countably cofinal maximal chains

Cite

@article{arxiv.1004.5542,
  title  = {Linear ROD subsets of Borel partial orders are countably cofinal in the Solovay model},
  author = {Vladimir Kanovei},
  journal= {arXiv preprint arXiv:1004.5542},
  year   = {2018}
}

Comments

5 pages

Linear ROD subsets of Borel partial orders are countably cofinal in the Solovay model

Abstract

Keywords

Cite

Comments

Related papers