{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101483"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101483","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Algebraically closed fields with characters; differential-henselian monotone valued differential fields","abstract":"This thesis consists of two unrelated research projects. In the first project we study the model theory of the 2-sorted structure (F, C; χ), where F is an algebraic closure of a finite field of characteristic p, C is the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. In the second project we study the model theory of the differential-henselian monotone valued differential fields. We also consider definability in differential-henselian monotone fields with c-map and angular component map.","abstract_html":"This thesis consists of two unrelated research projects. In the first project we study the model theory of the 2-sorted structure (F, C; χ), where F is an algebraic closure of a finite field of characteristic p, C is the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. In the second project we study the model theory of the differential-henselian monotone valued differential fields. We also consider definability in differential-henselian monotone fields with c-map and angular component map.","abstract_has_math":false,"creators":["Hakobyan, Tigran"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["van den Dries, Lou","Hieronymi, Philipp","Tserunyan, Anush","Walsberg, Erik"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-27T16:17:24Z","date_published":"2018-09-27T16:17:24Z","updated_at":"2026-07-22T22:24:40Z","subjects":["mathematical logic","model theory","quantifier elimination","NIP","fields","algebraically closed fields","characters","differential fields","valued fields","valued differential fields","d-henselian fields","monotone valued differential fields","Ax-Kochen-Ershov principle","Ax-Kochen principle"],"languages":["en"],"rights":["Copyright 2018 Tigran Hakobyan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101483","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["van den Dries, Lou","Hieronymi, Philipp","Tserunyan, Anush","Walsberg, Erik"]},{"key":"dc:creator","label":"Author","values":["Hakobyan, Tigran"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-27T16:17:24Z","2018-06-29","2018-08"]},{"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":["mathematical logic","model theory","quantifier elimination","NIP","fields","algebraically closed fields","characters","differential fields","valued fields","valued differential fields","d-henselian fields","monotone valued differential fields","Ax-Kochen-Ershov principle","Ax-Kochen principle"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Tigran Hakobyan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101483"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis consists of two unrelated research projects. In the first project we study the model theory of the 2-sorted structure (F, C; χ), where F is an algebraic closure of a finite field of characteristic p, C is the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. In the second project we study the model theory of the differential-henselian monotone valued differential fields. We also consider definability in differential-henselian monotone fields with c-map and angular component map.","Submission original under an indefinite embargo labeled 'Open Access'. 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No. of bitstreams: 4 HAKOBYAN-DISSERTATION-2018.pdf: 559980 bytes, checksum: 0d14a3e2453f887b35408c012b40f89b (MD5) Thesis - Tigran Hakobyan.zip: 91732 bytes, checksum: 2cad8ae2133200550b11360af0ae67d2 (MD5) LICENSE.txt: 4212 bytes, checksum: 289b1b0351de67a0c2565b35337f3e66 (MD5) PROQUEST_LICENSE.txt: 4558 bytes, checksum: af8bd922a20ee0ef89b0d8e422e26bc8 (MD5) Previous issue date: 2018-06-29"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Algebraically closed fields with characters; differential-henselian monotone valued differential fields"]}]}],"canonical_facts":{"dc:contributor":["van den Dries, Lou","Hieronymi, Philipp","Tserunyan, Anush","Walsberg, Erik"],"dc:creator":["Hakobyan, Tigran"],"dc:date":["2018-09-27T16:17:24Z","2018-06-29","2018-08"],"dc:description":["This thesis consists of two unrelated research projects. In the first project we study the model theory of the 2-sorted structure (F, C; χ), where F is an algebraic closure of a finite field of characteristic p, C is the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. In the second project we study the model theory of the differential-henselian monotone valued differential fields. We also consider definability in differential-henselian monotone fields with c-map and angular component map.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Tigran Hakobyan, accepted the attached license on 2018-06-25 at 13:13.","The student, Tigran Hakobyan, submitted this Dissertation for approval on 2018-06-25 at 16:33.","This Dissertation was approved for publication on 2018-06-29 at 10:02.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12611 on 2018-09-27 at 10:44:40","Made available in DSpace on 2018-09-27T16:17:24Z (GMT). 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