{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/115816"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/115816","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quantifier elimination and decidability of the theory of additive integer group augmented by predicates of multiplicative cyclic submonoids","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-14 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-14 without embargo terms","abstract_has_math":false,"creators":["Wang, Xiaoduo"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hieronymi, Philipp"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05","date_published":"2022-05","updated_at":"2026-07-22T22:24:55Z","subjects":["Model Theory","Logic","Number Theory"],"languages":["en","eng"],"rights":["Copyright 2022 Xiaoduo Wang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/115816","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hieronymi, Philipp"]},{"key":"dc:creator","label":"Author","values":["Wang, Xiaoduo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-05","2022-04-26"]},{"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":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Model Theory","Logic","Number Theory"]}]},{"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 Xiaoduo Wang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/115816"]}]},{"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 2022-11-14 without embargo terms","The student, Xiaoduo Wang, accepted the attached license on 2022-04-19 at 13:10.","The student, Xiaoduo Wang, submitted this Thesis for approval on 2022-04-19 at 13:17.","This Thesis was approved for publication on 2022-04-26 at 14:57.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17804 on 2022-11-14 at 17:33:55","In this thesis, we study an extension of the theory of the additive group of integers. To be more specific, if we let {q1, q2, ...} be an enumeration of all positive prime integers and for each positive prime integers q, let qN denote the set {qn : n ∈ N}, then we are interested in the theory Th(Z,+,−, 0, 1, qNi )i∈I, where I ⊆ N. We give a set of sentences T explicitly and show that T axiomatizes the theory using a back-and-forth system. We also investigate the extent of quantifier elimination of T and its decidability. In particular, we show that every formula in the language of groups is T-equivalent to a boolean combination of existential formulas, and we also show that the decidability of Th(Z,+,−, 0, 1, qNi )i∈I is equivalent to a number theoretical problem."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Quantifier elimination and decidability of the theory of additive integer group augmented by predicates of multiplicative cyclic submonoids"]}]}],"canonical_facts":{"dc:contributor":["Hieronymi, Philipp"],"dc:creator":["Wang, Xiaoduo"],"dc:date":["2022-05","2022-04-26"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-14 without embargo terms","The student, Xiaoduo Wang, accepted the attached license on 2022-04-19 at 13:10.","The student, Xiaoduo Wang, submitted this Thesis for approval on 2022-04-19 at 13:17.","This Thesis was approved for publication on 2022-04-26 at 14:57.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17804 on 2022-11-14 at 17:33:55","In this thesis, we study an extension of the theory of the additive group of integers. To be more specific, if we let {q1, q2, ...} be an enumeration of all positive prime integers and for each positive prime integers q, let qN denote the set {qn : n ∈ N}, then we are interested in the theory Th(Z,+,−, 0, 1, qNi )i∈I, where I ⊆ N. We give a set of sentences T explicitly and show that T axiomatizes the theory using a back-and-forth system. We also investigate the extent of quantifier elimination of T and its decidability. In particular, we show that every formula in the language of groups is T-equivalent to a boolean combination of existential formulas, and we also show that the decidability of Th(Z,+,−, 0, 1, qNi )i∈I is equivalent to a number theoretical problem."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/115816"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Xiaoduo Wang"],"dc:subject":["Model Theory","Logic","Number Theory"],"dc:title":["Quantifier elimination and decidability of the theory of additive integer group augmented by predicates of multiplicative cyclic submonoids"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:55Z"}