Itay Kaplan (Hebrew University of Jerusalem)
- Date
- Tuesday 22 February 2022
- Category
- Models and Sets Seminar
On large externally definable subsets in NIP
Joint work with Martin Bays and Pierre Simon
Suppose that $M$ is a model of an NIP theory, and $X$ an externally definable subset: for some elementary extension $N$ of $M$, and some $c$ from $N$, $X = \{a \in M : \phi(a,c) \text{ holds}\}$.
How large should $X$ be to contain an infinite $M$-definable subset? Chernikov and Simon asked whether aleph1 is enough. I will discuss this question and relate it to questions in model theory and infinite combinatorics.