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].
Characterizing forking in VC-minimal theories
Doctoral Dissertation
Abstract
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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 |
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Submission Date | 2012-05-25 |
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Record Visibility | Public |
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CotterS052012D.pdf | 506 KB | application/pdf | Public |
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