Logic Seminar

Please note that the time is PST

Given a class of groups, say the class of all countably infinite groups, it is natural to ask: what group properties are generic in the sense of Baire category in this class? For this question to make sense, we need a topology. In the case of countably infinite groups, a natural choice is the following: fix N as a common universe and identify every group on N with the group operation that defines it. These group operations form a Polish subspace in N^(N×N) . I will talk about generic group properties in this setting, and, if time permits, I will also say a few words about other settings and generic properties in various classes of topological groups.