Logic Seminar

Colin Jahel (TU Dresden)

When invariance implies exchangeability (and what it means for invariant Keisler measures)

Let M be a countable model-theoretic structure. We study the actions of Aut(M) on spaces of expansions of M and more precisely, the invariant probability measures under this action. In particular we are interested in understanding when Aut(M)-invariance actually implies S_\infty invariance. We obtain a nice classification for many classical structures. Finally we connect this to invariant Keisler measures, showing how for many structures, they must be S_\infty-invariant. We use this fact to illustrate the difference between two notion of smallness for formulas, forking and universal measure zero.

MC 5403