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https://hdl.handle.net/2142/86881
Description
Title
Model Theory of Valued Difference Fields
Author(s)
Azgin, Salih
Issue Date
2007
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
In this thesis we investigate the model theoretic properties of valued difference fields, that is, valued fields equipped with a distinguished automorphism. We carry out this study in two different contexts depending on the interaction between the valuation and the distinguished automorphism. In both contexts we obtain analogues of the classical results from the model theory of valued fields. We also present a treatment of valued fields in equal characteristic p > 0 as valued difference fields equipped with the Frobenius endomorphism.
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