Submission date: 26 May 2010.

Abstract:

In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called “uniform definability of types over finite sets” (UDTFS). We explore UDTFS and show how it relates to well-known properties in model theory. We recall that stable theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence. We then show that all dp-minimal theories have UDTFS.

Mathematics Subject Classification: 03C45

Keywords and phrases: UDTFS, dp-minimal, definability of types, NIP, dependent, indiscernible sequences, VC-density

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