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Model Theory Seminar
Hunter Johnson
John Jay College, CUNY
Title: UDTFS, neighborliness and coherence

Abstract: This talk will explore an idea currently gaining attention in model theory, namely that properties of stable formulas hold of NIP formulas, provided that the word "finite" is judiciously inserted into their definitions. Primarily we will be interested in a formula having uniform definability of types over finite sets (UDTFS). This condition is well known to imply NIP; much effort has gone into attempts to establish the converse, both in computer science and in model theory, but the question remains open. The most general class of "classical" theories currently known to posses UDTFS are the dp-minimal theories. We discuss some new conditions, namely "coherence" and "neighborliness" which are sufficient for UDTFS. They extend the dp-minimal and o-minimal approaches, respectively. We will also try to show applications of UDTFS to the study of VC density, and trace its pre-history in computational learning theory.

Date: Saturday, January 1, 2011
Time: 5:00 pm
Location: Wean Hall 8220
Submitted by:  Grossberg