Characterizing forking in VC-minimal theories

Doctoral Dissertation

Abstract

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].

Attributes

Attribute NameValues
URN
  • etd-05252012-135318

Author Sarah Cotter
Advisor Sergei Starchenko
Contributor Julia Knight, Committee Member
Contributor Joseph Flenner, Committee Member
Contributor Peter Cholak, Committee Member
Contributor Sergei Starchenko, Committee Chair
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2012-05-10

Submission Date 2012-05-25
Country
  • United States of America

Subject
  • model theory

  • Mathematical logic

  • VC-minimality

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility and Access Public
Content License
  • All rights reserved

Departments and Units

Files

Please Note: You may encounter a delay before a download begins. Large or infrequently accessed files can take several minutes to retrieve from our archival storage system.