2026-09-23T01:40:32Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/105647 2023-07-11 col_2142_16340 col_2142_5131 com_2142_16339 com_2142_8903 com_2142_5130

http://hdl.handle.net/2142/105647 en Copyright 2019 Travis Nell Model Theory of Ordered Structures, Distality, NIP, Dependent Theories Distality and pairs text text Hieronymi, Philipp van den Dries, Lou Tserunyan, Anush Walsberg, Erik Nell, Travis 2019-11-26T20:33:53Z 2019-11-26T20:33:53Z 2019-07-05 2019-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms The student, Travis Nell, accepted the attached license on 2019-07-03 at 18:22. The student, Travis Nell, submitted this Dissertation for approval on 2019-07-03 at 18:26. This Dissertation was approved for publication on 2019-07-05 at 15:41. DSpace SAF Submission Ingestion Package generated from Vireo submission #14165 on 2019-11-26 at 12:51:08 Made available in DSpace on 2019-11-26T20:33:53Z (GMT). No. of bitstreams: 2 NELL-DISSERTATION-2019.pdf: 127394420 bytes, checksum: af7f7b123c7c21914682670ff01a95cc (MD5) LICENSE.txt: 4208 bytes, checksum: e04803838bc11e488367fdfc86a30adf (MD5) Previous issue date: 2019-07-05 application/pdf Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.