# A Local Characterization of VC-minimality

## Uri Andrews

### University of Wisconsin

(Work joint with Vincent Guingona.) I’ll talk about a problem in the intersection of computable model theory and classical model theory. The notion of VC-minimality, though intriguing, has proven very difficult to work with. It has even been difficult to check whether familiar examples are VC-minimal. This has led model theorists (chiefly my co-author) to ask whether there was a “local” (read “simpler”) characterization of VC-minimality. I suggested a computable model theoretic version of this question in terms of the index set of VC-minimality. We answered this question by giving a local characterization of VC-minimality, and we showed that VC-minimality is a Π^{0}_{4}-complete notion.

Uri Andrews received his Ph.D. from the University of California-Berkeley in 2010, as a student of Tom Scanlon, and subsequently took up an assistant professorship (now tenure-track) at the University of Wisconsin. He studies computable model theory, blending techniques from model theory and computability theory.