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arXiv:1004.5542 [math.LO]AbstractReferencesReviewsResources

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

Vladimir Kanovei

Published 2010-04-30, updated 2010-06-05Version 2

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.

Comments: 5 pages
Categories: math.LO
Subjects: 03E15
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