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Characterizing forking in VC-minimal theories

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posted on 2012-05-25, 00:00 authored by Sarah Cotter
We consider the class of VC-minimal theories, as introduced by Adler in [2]. After covering some basic results, including a notion of generic types, we consider two kinds of VC-minimal theories: those whose generating directed families are unpackable and almost unpackable. We introduce two new decompositions of definable sets in VC-minimal theories, the layer decomposition and the irreducible decomposition, which allow for more precision than the standard Swiss cheese decompositon with regard to parameters. Finally, after introducing a slight generalization of the classical notions of forking and dividing, we prove that in any VC-minimal or quasi-VC-minimal theory whose generating family is unpackable or almost unpackable, forking of formulae over a model M is equivalent to containment in a global M -definable type, generalizing a result of Dolich on o-minimal theories in [8].

History

Date Modified

2017-06-05

Defense Date

2012-05-10

Research Director(s)

Sergei Starchenko

Committee Members

Julia Knight Joseph Flenner Peter Cholak

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Language

  • English

Alternate Identifier

etd-05252012-135318

Publisher

University of Notre Dame

Program Name

  • Mathematics (MATH)

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