Logic Seminar - Ori Segal

Wed, 11/11/202011:15-13:00
Meeting ID: 868 3879 6860 Passcode: 175603

Boolean Types in Dependent Theories
(Joint work with Itay Kaplan and Saharon Shelah)

Abstract: Complete types, seen as ultrafilters, are naturally equivalent to Boolean homomorphisms to {0,1}.
The notion of a complete type can thus be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra to each formula, and this notion is particularily well behaved when the ambient theory has NIP.
I will show that this notion generalizes, in a sense, both complete types and Keisler measures.
In particular, the notion of smoothness can be generalized to Boolean types, and I will show that in NIP theories, Boolean types can be extended to smooth Boolean types, and deduce the same (known) result for Keisler measures.
All concepts and background material will be explained in the lecture.