Title:  Limits of sequences of finite structures in monadically stable theories

Speaker：Sam Braunfeld (Charles University)

Time: 2025/04/03 16:00-17:00

Zoom room: 717 463 6082

Organizer: Kyle Gannon (BICMR)

Abstract：

　　In search of a notion of graph limit for sequences of sparse graphs, Nešetřil and Ossona de Mendez introduced first-order convergence for sequences of finite structures (requiring that for every formula, the probability that it is satisfied by a tuple chosen uniformly at random converges) and corresponding analytic limit objects called modeling limits. A modeling limit is a Borel structure, i.e. its domain is a standard Borel space and every parameter-definable relation is Borel, equipped with a probability measure assigning the appropriate limiting value to definable relations (or rather, a sequence of measures for increasing powers of the structure). We show that a modeling limit can be constructed for any convergent sequence of finite structures from a monadically stable class. Behind this is a theorem about realizing measures from sufficiently saturated models of a monadically stable theory in Borel models. Joint work with Jarik Nešetřil and Patrice Ossona de Mendez.