{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/117798"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/117798","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Describing generic elements of Polish groups","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled &#x27;Open Access&#x27;. The submission was exported from vireo on 2023-04-12 without embargo terms","abstract_has_math":false,"creators":["Ihli, Dakota Thor"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Tserunyan, Anush","Solecki, Sławomir","Albin, Pierre","Oikhberg, Timur"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12","date_published":"2022-12","updated_at":"2026-07-22T22:24:56Z","subjects":["Polish Groups","Generic Elements","Conjugacy Classes","Automorphism Groups","Random Poset","Absolutely Continuous","Topological Rank"],"languages":["en","eng"],"rights":["Copyright 2022 Dakota Thor Ihli"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/117798","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Tserunyan, Anush","Solecki, Sławomir","Albin, Pierre","Oikhberg, Timur"]},{"key":"dc:creator","label":"Author","values":["Ihli, Dakota Thor"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-12","2022-12-02"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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":["Polish Groups","Generic Elements","Conjugacy Classes","Automorphism Groups","Random Poset","Absolutely Continuous","Topological Rank"]}]},{"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 2022 Dakota Thor Ihli"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/117798"]}]},{"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 2023-04-12 without embargo terms","The student, Dakota Ihli, accepted the attached license on 2022-11-29 at 15:03.","The student, Dakota Ihli, submitted this Dissertation for approval on 2022-11-29 at 16:48.","This Dissertation was approved for publication on 2022-12-02 at 13:00.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18670 on 2023-04-12 at 07:35:40","For a Polish group G, we say an element g ∈ G is generic if it has a comeagre conjugacy class. We examine the questions of existence, and of behavior, for generic elements in two particular Polish groups. Firstly, we give a concrete model-theoretic characterization of the generic automorphism of the countable universal ultrahomogeneous partial order, also called the random poset. Secondly, we prove that the group of order-preserving, absolutely continuous homeomorphisms of the interval admits generic elements, and we give a concrete characterization. Additionally, we show that this group is generically topologically 2-generated; that is, for a comeagre set of pairs (f,g) of absolutely continuous interval homeomorphisms, the subgroup <f,g> is dense."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Describing generic elements of Polish groups"]}]}],"canonical_facts":{"dc:contributor":["Tserunyan, Anush","Solecki, Sławomir","Albin, Pierre","Oikhberg, Timur"],"dc:creator":["Ihli, Dakota Thor"],"dc:date":["2022-12","2022-12-02"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","The student, Dakota Ihli, accepted the attached license on 2022-11-29 at 15:03.","The student, Dakota Ihli, submitted this Dissertation for approval on 2022-11-29 at 16:48.","This Dissertation was approved for publication on 2022-12-02 at 13:00.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18670 on 2023-04-12 at 07:35:40","For a Polish group G, we say an element g ∈ G is generic if it has a comeagre conjugacy class. We examine the questions of existence, and of behavior, for generic elements in two particular Polish groups. Firstly, we give a concrete model-theoretic characterization of the generic automorphism of the countable universal ultrahomogeneous partial order, also called the random poset. Secondly, we prove that the group of order-preserving, absolutely continuous homeomorphisms of the interval admits generic elements, and we give a concrete characterization. Additionally, we show that this group is generically topologically 2-generated; that is, for a comeagre set of pairs (f,g) of absolutely continuous interval homeomorphisms, the subgroup <f,g> is dense."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/117798"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Dakota Thor Ihli"],"dc:subject":["Polish Groups","Generic Elements","Conjugacy Classes","Automorphism Groups","Random Poset","Absolutely Continuous","Topological Rank"],"dc:title":["Describing generic elements of Polish groups"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:56Z"}