2
$\begingroup$

For a countable ordinal $\eta$ and an ordinal $\gamma$ let $\langle P_\alpha, \dot{Q}_\alpha \colon \alpha < \gamma \rangle$ be an RCS iteration with RCS limit $P_\gamma$, such that

  • $\Vdash_\alpha \dot{Q}_\alpha$ is $\eta$-semi-proper;
  • $\Vdash_{\alpha +1} \vert P_\alpha \vert \leqslant \aleph_1$.

Is then the RCS limit $P_\gamma$ also $\eta$-semi-proper?

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ Isn't this what Shelah's iteration theorem for RCS says? $\endgroup$
    – Monroe Eskew
    Commented Aug 20, 2015 at 19:47
  • 2
    $\begingroup$ If you ignore the $\eta$, or set $\eta = 1$, then it's Shelah's theorem. Of course, increasing $\eta$ only strengthens the hypothesis. $\endgroup$
    – Paul Larson
    Commented Aug 20, 2015 at 19:50
  • $\begingroup$ Sorry, I am not so familiar with the terminology. Do you mean to ask whether $P_\gamma$ is $\eta$-semi-proper? $\endgroup$
    – Monroe Eskew
    Commented Aug 20, 2015 at 20:06

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .