Friday, October 7, 2022 — 10:30 AM EDT

Leo Jimenez, Department of Pure Math, University of Waterloo

"Expansions of the group of integers"

Consider the group of integers. As far as model theory goes, this is one of the tamest structures out there (superstable U-rank one). Now pick a non-definable subset S, and add it as a unary predicate. How tame (or wild) is the resulting theory? In a recent preprint, joint with Conant, d'Elbee, Halevi and Rideau-Kikuchi, we show that it can be as tame (or wild) as one wants. In this talk, I will discuss the proof of this, which involves new results on expanding the structure of stably embedded sets, as well as the new notion of algebraic embeddedness.

MC 5403

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