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Type of Document Dissertation Author Heidenreich, Jacob Robert Author's Email Address heidenrj@gvsu.edu URN etd-07192005-113657 Title Stability Theory Modulo a Predicate Degree Doctor of Philosophy Department Mathematics Advisory Committee
Advisor Name Title Peter M. Kogge Committee Chair David Marker Committee Member Peter Cholak Committee Member Steven Buechler Committee Member Tim Bays Committee Member Keywords
- stability theory
- classification theory
- descriptive set theory
- real normed vector spaces
Date of Defense 2005-06-21 Availability restricted Abstract 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).Files
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