{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86891"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86891","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Model Theory of Differentially Closed Fields With Several Commuting Derivations","abstract":"In this thesis we deal with the model theory of differentially closed fields of characteristic zero with several commuting derivations. The questions we consider belong to the area of geometric stability theory. First we observe that the only known lower bound for the Lascar rank of types in differentially closed fields, announced in a paper of McGrail, is false. This gives us a new class of regular types. Then we show that the generic type of the heat variety, which is one of these new types, is locally modular. So, unlike the case of ordinary differential fields, the additive group of a partial differential field has locally modular subgroups. We also classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are nonorthogonal to fields.","abstract_html":"In this thesis we deal with the model theory of differentially closed fields of characteristic zero with several commuting derivations. The questions we consider belong to the area of geometric stability theory. First we observe that the only known lower bound for the Lascar rank of types in differentially closed fields, announced in a paper of McGrail, is false. This gives us a new class of regular types. Then we show that the generic type of the heat variety, which is one of these new types, is locally modular. So, unlike the case of ordinary differential fields, the additive group of a partial differential field has locally modular subgroups. We also classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are nonorthogonal to fields.","abstract_has_math":false,"creators":["Suer, Sonat"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Pillay, Anand"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:02Z","date_published":"2015-09-28T15:20:02Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3290394"],"render_values":[{"text":"(MiAaPQ)AAI3290394","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86891","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pillay, Anand"]},{"key":"dc:creator","label":"Author","values":["Suer, Sonat"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:02Z","10000-01-01","2007"]},{"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":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86891","(MiAaPQ)AAI3290394"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we deal with the model theory of differentially closed fields of characteristic zero with several commuting derivations. 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The questions we consider belong to the area of geometric stability theory. First we observe that the only known lower bound for the Lascar rank of types in differentially closed fields, announced in a paper of McGrail, is false. This gives us a new class of regular types. Then we show that the generic type of the heat variety, which is one of these new types, is locally modular. So, unlike the case of ordinary differential fields, the additive group of a partial differential field has locally modular subgroups. We also classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are nonorthogonal to fields.","Made available in DSpace on 2015-09-28T15:20:02Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290394.pdf: 1630030 bytes, checksum: b673089caf15f66694745ba0a5a8dd97 (MD5) Previous issue date: 2007","Embargo set by: Seth Robbins for item 88172 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","55 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007."],"dc:identifier":["http://hdl.handle.net/2142/86891","(MiAaPQ)AAI3290394"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Model Theory of Differentially Closed Fields With Several Commuting Derivations"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}