Logic Seminar

Given an Lω1ωLω1ω-sentence φφ in a countable language, we call an ergodic S∞S∞-invariant probability measure on the Borel space of countable models of φφ (having fixed underlying set) an ergodic model of φφ. I will discuss the number of ergodic models of such a sentence φφ, including the case when φφ is a Scott sentence. This is joint work with N. Ackerman, C. Freer, A. Kruckman and A. Kwiatkowska.