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https://hdl.handle.net/2142/86816
Description
Title
T-Levels and T-Convexity
Author(s)
Tyne, James Michael
Issue Date
2003
Doctoral Committee Chair(s)
van den Dries, Lou
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
"Let R be a model of an o-minimal theory T. We define the ""T-levels"" of R and explore their connection to tame substructures of R , subject to a few easily satisfied assumptions. This leads to results about the theory of models of T equipped with a T-convex subset, and to answers to some open questions about o-minimal expansions of real closed fields equipped with a T-convex subring. Specifically, we establish the Valuation and Residue Properties for power bounded o-minimal expansions of real closed fields equipped with a T-convex subring."
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