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Stability Theory Modulo a Predicate
thesis
posted on 2005-07-19, 00:00 authored by Jacob Robert HeidenreichIn 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).
History
Date Modified
2017-06-02Defense Date
2005-06-21Research Director(s)
Peter M. KoggeCommittee Members
Peter Cholak David Marker Steven Buechler Tim BaysDegree
- Doctor of Philosophy
Degree Level
- Doctoral Dissertation
Language
- English
Alternate Identifier
etd-07192005-113657Publisher
University of Notre DameProgram Name
- Mathematics
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