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https://hdl.handle.net/2142/86831
Description
Title
Stability in Geometric Theories
Author(s)
Gagelman, Jerry
Issue Date
2004
Doctoral Committee Chair(s)
Pillay, Anand
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
The second question is answered for o-minimal structures that eliminate imaginaries. It is proved that for any structure D whose theory is o-minimal and eliminates imaginaries, any stable group interpretable in D is totally transcendental with finite Morley rank. A strengthening of Buechler's Dichotomy Theorem is also proved for stable (viz. superstable) structures that are interpretable in D.
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