29 settembre 2023, 16.00-17.00 (Location to be specified.)
B. Yaacov (Université Claude Bernard - Lyon 1) "Coding first order theories, and their separable models, in topological groups and groupoids".
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A result of Coquand (sometimes wrongly attributed to Ahlbrandt and Ziegler), asserts that two countably categorical theories (always in a countable language) are biinterpretable if and only if their countable models have the same topological automorphism groups.
This was later extended to separably categorical theories in continuous logic, and served as a starting point for several papers relating model theoretic properties of separably categorical theories and dynamical properties of Roelcke-precompact Polish groups (works by Kaichouh, Ibarlucía, Tsankov, and the speaker, among others).
From a model-theoretic perspective, it is natural to ask whether any of this can be extended beyond the realm of separably categorical theories. We can answer positively for Coquand's result : to every theory T (in a countable language) we can associate a Polish topological groupoid G(T) that serves as a complete invariant for the bi-interpretation class of T . This was done first in classical logic, and then, overcoming some surprising additional complications, in continuous logic.
I will present the main ideas behind this last result, as well as some new questions that it raises.
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