On uniform definability of types over finite sets

2010/05/26 by Vincent Guingona, Guingona, Vincent · 1 citation
Computer Science · Mathematics · #03C45 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1005.4924

openalex publication_date 2010/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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