{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/129922"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/129922","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Uniform bounds in D-minimal structures","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_has_math":false,"creators":["Farris, Madie"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hieronymi, Philipp","van den Dries, Lou","Castle, Ben","Miller, Chris"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-07-08","date_published":"2025-07-08","updated_at":"2026-07-22T22:25:06Z","subjects":["D-minimality","Model Theory","O-minimality"],"languages":["en","eng"],"rights":["Copyright 2025 Madie Farris"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/129922","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","Castle, Ben","Miller, Chris"]},{"key":"dc:creator","label":"Author","values":["Farris, Madie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-07-08","2025-08"]},{"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 Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["D-minimality","Model Theory","O-minimality"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Madie Farris"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/129922"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Madie Farris, accepted the attached license on 2025-07-07 at 09:52.","The student, Madie Farris, submitted this Dissertation for approval on 2025-07-07 at 09:58.","This Dissertation was approved for publication on 2025-07-08 at 13:32.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22423 on 2025-10-20 at 20:15:04","O-minimality as a classification of the topological tameness of a structure has been extensively studied since its introduction in 1982. Many generalizations and variations of o-minimality have since been introduced and studied as well. In this thesis we focus on one particular generalization: d-minimality. We establish some of the first results on d-minimality that truly mirror those of o-minimality. The most central of which is the equivalence of d-minimality and strong d-minimality. In the process of proving this equivalence we develop a d-minimal version of cell decomposition, one of the most important results in o-minimality. In Chapter 1 we discuss the overarching project of tame topology, and situate d-minimality within this context. We define a grid, the object that we will use to decompose sets in d-minimal structures, and our main results, including the aforementioned decomposition theorem. Chapter 2 is spent establishing some preliminary facts that are used throughout this thesis. In Chapter 3 we motivate our choice of definition for grids by working through an example of a grid decomposition, and compare this decomposition to a previously known result for strongly d-minimal structures. We develop the theory of grids (and cells and stacks which are used to build grids) in Chapter 4. We put all of these pieces together in Chapter 5 where we prove our main results. In Chapter 6 we extend these results to a more general setting. Lastly, we discuss future applications of our main results in Chapter 7."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Uniform bounds in D-minimal structures"]}]}],"canonical_facts":{"dc:contributor":["Hieronymi, Philipp","van den Dries, Lou","Castle, Ben","Miller, Chris"],"dc:creator":["Farris, Madie"],"dc:date":["2025-07-08","2025-08"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Madie Farris, accepted the attached license on 2025-07-07 at 09:52.","The student, Madie Farris, submitted this Dissertation for approval on 2025-07-07 at 09:58.","This Dissertation was approved for publication on 2025-07-08 at 13:32.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22423 on 2025-10-20 at 20:15:04","O-minimality as a classification of the topological tameness of a structure has been extensively studied since its introduction in 1982. Many generalizations and variations of o-minimality have since been introduced and studied as well. In this thesis we focus on one particular generalization: d-minimality. We establish some of the first results on d-minimality that truly mirror those of o-minimality. The most central of which is the equivalence of d-minimality and strong d-minimality. In the process of proving this equivalence we develop a d-minimal version of cell decomposition, one of the most important results in o-minimality. In Chapter 1 we discuss the overarching project of tame topology, and situate d-minimality within this context. We define a grid, the object that we will use to decompose sets in d-minimal structures, and our main results, including the aforementioned decomposition theorem. Chapter 2 is spent establishing some preliminary facts that are used throughout this thesis. In Chapter 3 we motivate our choice of definition for grids by working through an example of a grid decomposition, and compare this decomposition to a previously known result for strongly d-minimal structures. We develop the theory of grids (and cells and stacks which are used to build grids) in Chapter 4. We put all of these pieces together in Chapter 5 where we prove our main results. In Chapter 6 we extend these results to a more general setting. Lastly, we discuss future applications of our main results in Chapter 7."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/129922"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Madie Farris"],"dc:subject":["D-minimality","Model Theory","O-minimality"],"dc:title":["Uniform bounds in D-minimal structures"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:06Z"}