Aspects of stability in simple theories

Doctoral Dissertation

Abstract

Simple theories are a strict extension of stable theories for which non-forking independence is a nice independence relation. However, not much is known about how the simple unstable theories differ from the strictly stable ones. This work looks at three aspects of simple theories and uses them to give a better picture of the differences between the two classes. First, we look at the property of weakly eliminating hyperimaginaries and show that it is equivalent to forking and thorn-forking independence coinciding. Second, we look at the stable forking conjecture}, a strong statement asserting that simple unstable theories have an essentially stable “core,” and prove that it holds between elements having SU-rank 2 and finite SU-rank. Third, we consider a property on indiscernible sequences that is known to hold in every stable theory, and show it holds on, at most, a subset of simple theories out of all possible first order theories.

Attributes

Attribute NameValues
URN
  • etd-04202012-101906

Author Donald A Brower
Advisor Steven Buechler
Contributor Cameron Hill, Committee Member
Contributor Steven Buechler, Committee Chair
Contributor Julia Knight, Committee Member
Contributor Sergei Starchenko, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2012-04-12

Submission Date 2012-04-20
Country
  • United States of America

Subject
  • indiscernible sequence

  • classification theory

  • model theory

  • hyperimaginary

  • Logic

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility and Access Public
Content License
  • All rights reserved

Departments and Units

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