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

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

2010-04-30

arxiv.org/abs/1004.5542v2

Mathematics

Logic

5 pages

Scientific paper

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.

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