5
$\begingroup$

Definition. Whenever $M$ is a countable model of $\mathrm{ZFC}$ (not necessarily well-founded) write $\mathrm{Inn}(M)$ for the poset of inner models of $M$ ordered by inclusion.

Question. For which countably infinite posets $P$ does there exist a model $M$ of $\mathrm{ZFC}$ such that $P \cong \mathrm{Inn}(M)$?

Partial answers and/or references appreciated. Also: if we need to assume that $M$ is well-founded (or even transitive) to get a useful answer, then so be it.

$\endgroup$
1

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.