{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/100890"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/100890","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Truncation in differential Hahn fields","abstract":"Being closed under truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation we show that generalized series fields with truncation as an extra primitive yields undecidability in several settings. Our main results, however, concern the robustness of being truncation closed in generalized series fields equipped with a derivation, and under extension procedures that involve this derivation. In the last chapter we study this in the ambient field T of logarithmic-exponential transseries. It leads there to a theorem saying that under a natural ``splitting'' condition the Liouville closure of a truncation closed differential subfield of T is again truncation closed.","abstract_html":"Being closed under truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation we show that generalized series fields with truncation as an extra primitive yields undecidability in several settings. Our main results, however, concern the robustness of being truncation closed in generalized series fields equipped with a derivation, and under extension procedures that involve this derivation. In the last chapter we study this in the ambient field T of logarithmic-exponential transseries. It leads there to a theorem saying that under a natural ``splitting'' condition the Liouville closure of a truncation closed differential subfield of T is again truncation closed.","abstract_has_math":false,"creators":["Camacho Ahumada, Santiago"],"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","Tserunyan, Anush","Walsberg, Erik","van den Dries, Lou"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-04T20:26:30Z","date_published":"2018-09-04T20:26:30Z","updated_at":"2026-07-22T22:24:38Z","subjects":["Valued Fields","Transseries","Truncation","Differential Algebra","Hahn Fields"],"languages":["en"],"rights":["Copyright 2018 Santiago Camacho Ahumada"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/100890","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hieronymi, Philipp","Tserunyan, Anush","Walsberg, Erik","van den Dries, Lou"]},{"key":"dc:creator","label":"Author","values":["Camacho Ahumada, Santiago"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-04T20:26:30Z","2018-01-10","2018-05"]},{"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":["Valued Fields","Transseries","Truncation","Differential Algebra","Hahn Fields"]}]},{"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 Santiago Camacho Ahumada"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/100890"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Being closed under truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation we show that generalized series fields with truncation as an extra primitive yields undecidability in several settings. Our main results, however, concern the robustness of being truncation closed in generalized series fields equipped with a derivation, and under extension procedures that involve this derivation. In the last chapter we study this in the ambient field T of logarithmic-exponential transseries. It leads there to a theorem saying that under a natural ``splitting'' condition the Liouville closure of a truncation closed differential subfield of T is again truncation closed.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-08-31 without embargo terms","The student, Santiago Camacho Ahumada, accepted the attached license on 2018-01-05 at 15:43.","The student, Santiago Camacho Ahumada, submitted this Dissertation for approval on 2018-01-05 at 15:52.","This Dissertation was approved for publication on 2018-01-10 at 16:23.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12007 on 2018-08-31 at 17:08:02","Made available in DSpace on 2018-09-04T20:26:30Z (GMT). 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Nevertheless, in Chapter 4 of this dissertation we show that generalized series fields with truncation as an extra primitive yields undecidability in several settings. Our main results, however, concern the robustness of being truncation closed in generalized series fields equipped with a derivation, and under extension procedures that involve this derivation. In the last chapter we study this in the ambient field T of logarithmic-exponential transseries. It leads there to a theorem saying that under a natural ``splitting'' condition the Liouville closure of a truncation closed differential subfield of T is again truncation closed.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-08-31 without embargo terms","The student, Santiago Camacho Ahumada, accepted the attached license on 2018-01-05 at 15:43.","The student, Santiago Camacho Ahumada, submitted this Dissertation for approval on 2018-01-05 at 15:52.","This Dissertation was approved for publication on 2018-01-10 at 16:23.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12007 on 2018-08-31 at 17:08:02","Made available in DSpace on 2018-09-04T20:26:30Z (GMT). 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