Characterizing forking in VC-minimal theories

Doctoral Dissertation


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].


Attribute NameValues
  • 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
  • United States of America

  • model theory

  • Mathematical logic

  • VC-minimality

  • University of Notre Dame

  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units


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