Distality and pairs

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Nell, Travis

Contributors dc:contributor

• Hieronymi, Philipp
• van den Dries, Lou
• Tserunyan, Anush
• Walsberg, Erik

• Model Theory of Ordered Structures, Distality, NIP, Dependent Theories

Statement dc:rights

• Copyright 2019 Travis Nell

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/105647

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/105647