  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.
