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Title:Distality and pairs
Author(s):Nell, Travis
Director of Research:Hieronymi, Philipp
Doctoral Committee Chair(s):van den Dries, Lou
Doctoral Committee Member(s):Tserunyan, Anush; Walsberg, Erik
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2019-07-05
Type:Text
URI:http://hdl.handle.net/2142/105647
Rights Information:Copyright 2019 Travis Nell
Date Available in IDEALS:2019-11-26
Date Deposited:2019-08


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