Distality and pairs

[摘要] 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.

[关键词] Model Theory of Ordered Structures, Distality, NIP, Dependent Theories