Stability Theory Modulo a Predicate

Doctoral Dissertation


In this thesis we develop the analysis of the structure of a model, modulo the structure induced by a part of the model interpreting a predicate, P. We develop the “Morley Rank Modulo a Predicate”, PMR, and define an independence relation based on this rank. We analyze this relation in a nice setting (where every formula has PMR) in terms of the eight axioms of stability theory. We prove a dichotomy theorem classifying PMR-Minimal structures and a two-cardinal result. Finally, we give a classification of the norms one can place on a finite dimensional vector space over the reals (up to model-theoretic equivalence).


Attribute NameValues
  • etd-07192005-113657

Author Jacob Robert Heidenreich
Advisor Peter M. Kogge
Contributor Peter Cholak, Committee Member
Contributor David Marker, Committee Member
Contributor Steven Buechler, Committee Member
Contributor Tim Bays, Committee Member
Contributor Peter M. Kogge, Committee Chair
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2005-06-21

Submission Date 2005-07-19
  • United States of America

  • stability theory

  • real normed vector spaces

  • classification theory

  • descriptive set theory

  • University of Notre Dame

  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units


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.