Amador Martin-Pizarro - Stability and the strong Erdős-Hajnal property

jeudi 21 mai 2026, 14:00 → 15:00 Europe/Paris

112 (ICJ)

Abstract. A bipartite graph R on U x V has the strong Erdős-Hajnal Property if there exits a constant delta>0 such that for any finite subsets A of U and B of V, there exists an R-homogeneous pair (A_0, B_0), where A_0, resp. B_0, is a subset of A, resp. of B, of relative density at least delta.

Chernikov and Starchenko showed that every bipartite graph definable in a distal theory has the strong Erdős-Hajnal Property. Stable theories cannot be distal (but many relevant stable theories are reducts of distal theories, and thus inherit the strong Erdős-Hajnal Property). In this talk, we will present an elementary proof of the strong Erdős-Hajnal Property for a certain class of stable theories.