Director of Research (if dissertation) or Advisor (if thesis)
Hieronymi, Philipp
Doctoral Committee Chair(s)
van den Dries, Lou
Committee Member(s)
Tserunyan, Anush
Walsberg, Erik
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Model Theory of Ordered Structures, Distality, NIP, Dependent Theories
Abstract
This thesis studies certain expansions of o-minimal structures by unary predicates. The primary motivating question is that of the model theoretic property of distality, a property introduced by Simon in order to classify ordered versus stable behavior in a dependent (NIP) theory. We classify certain commonly known expansions of o-minimal structures as distal or non-distal, show certain non-distal examples can be expanded to distal structures, classify non-distal behavior in terms of predicate boundedness, and show certain examples can be expanded to be dependent and not admit a distal expansion.
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