{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105647"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105647","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Distality and pairs","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Nell, Travis"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hieronymi, Philipp","van den Dries, Lou","Tserunyan, Anush","Walsberg, Erik"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-26T20:33:53Z","date_published":"2019-11-26T20:33:53Z","updated_at":"2026-07-22T22:24:44Z","subjects":["Model Theory of Ordered Structures, Distality, NIP, Dependent Theories"],"languages":["en"],"rights":["Copyright 2019 Travis Nell"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105647","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hieronymi, Philipp","van den Dries, Lou","Tserunyan, Anush","Walsberg, Erik"]},{"key":"dc:creator","label":"Author","values":["Nell, Travis"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11-26T20:33:53Z","2019-07-05","2019-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Model Theory of Ordered Structures, Distality, NIP, Dependent Theories"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Travis Nell"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105647"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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'. 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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). 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