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I am curious about the open problems which are between model theory and dynamical system. I mean the open problems that are interesting for both groups and there are some evidences showing there might be a nice interaction between model theory and dynamical systems. Thank you!

Any references would be appreciated!

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    $\begingroup$ Self-promotion: here's one dynamical open model-theoretic question. $\endgroup$
    – YCor
    Jul 9, 2021 at 20:38
  • $\begingroup$ Depending on what you mean by a "dynamical system", Vaught's conjecture might be the canonical example. $\endgroup$
    – tomasz
    Jul 10, 2021 at 23:13
  • $\begingroup$ If by a "dynamical system" you mean a $\mathbf Z$-action, this is much more restricted. Otherwise, there are lots of problems and conjectures related to model-theoretic group actions (of type-definable groups or of automorphism groups). $\endgroup$
    – tomasz
    Jul 10, 2021 at 23:15
  • $\begingroup$ I actually meant Z-action! $\endgroup$
    – Alex Israel
    Jul 10, 2021 at 23:32
  • $\begingroup$ Not a $\Bbb Z$-action but here is an important one: let $\mathcal F$ be a Fraïssé class in a finite relational language $L$ and let $\Bbb F$ be its Fraïssé limit. Must $\mathrm{Aut}(\Bbb F)$ have a metrizable universal minimal flow? More generally in the last ~15 years there has been a lot of interest in this kind of questions following the pubblication of the Kechris-Pestov-Todorcevic correspondence $\endgroup$
    – Alessandro Codenotti
    Jul 20, 2021 at 13:46

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