Algebra Seminar talk
2026-06-12
Mohandes Grilj
Coquand’s Theorem
Abstract:
Given a countable set $A$ and model-theoretic structure $\mathbb{A}$ on $A$, a natural question that arises is, to what extent does $\mathrm{Aut}(\mathbb{A})$, seen as a topologically closed subgroup of $\mathrm{Sym}(A)$, determine the structure $\mathbb{A}$. Coquand’s Theorem tells us that for $\omega$-categorical structures in a countable language, $\mathrm{Aut}(\mathbb{A})$ determines $\mathbb{A}$ up to a notion of bi-interpretability.