{"id":"https://openalex.org/W7113906556","doi":"https://doi.org/10.1145/3761668.3761673","title":"Formal Verification of the Equivalence Between Dedekind's Fundamental Theorem and the Supremum Theorem Based on Axiomatic Set Theory","display_name":"Formal Verification of the Equivalence Between Dedekind's Fundamental Theorem and the Supremum Theorem Based on Axiomatic Set Theory","publication_year":2025,"publication_date":"2025-06-13","ids":{"openalex":"https://openalex.org/W7113906556","doi":"https://doi.org/10.1145/3761668.3761673"},"language":null,"primary_location":{"id":"doi:10.1145/3761668.3761673","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3761668.3761673","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3761668.3761673","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 17th International Conference on Computer Modeling and Simulation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3761668.3761673","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ce Zhang","orcid":"https://orcid.org/0009-0002-2261-2676"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ce Zhang","raw_affiliation_strings":["Beijing University of Posts and Telecommunications, School of Electronic Engineering, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0002-2261-2676","affiliations":[{"raw_affiliation_string":"Beijing University of Posts and Telecommunications, School of Electronic Engineering, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"last","author":{"id":null,"display_name":"Wensheng Yu","orcid":"https://orcid.org/0000-0002-3832-2748"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wensheng Yu","raw_affiliation_strings":["Beijing University of Posts and Telecommunications, School of Electronic Engineering, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3832-2748","affiliations":[{"raw_affiliation_string":"Beijing University of Posts and Telecommunications, School of Electronic Engineering, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I139759216"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"23","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.5720000267028809,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.5720000267028809,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.07620000094175339,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.04830000177025795,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.6413999795913696},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6057999730110168},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.5432000160217285},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5131000280380249},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.4934999942779541},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4830999970436096},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4814000129699707},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.4763000011444092},{"id":"https://openalex.org/keywords/g\u00f6dels-completeness-theorem","display_name":"G\u00f6del's completeness theorem","score":0.4706999957561493},{"id":"https://openalex.org/keywords/compactness-theorem","display_name":"Compactness theorem","score":0.4325000047683716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6435999870300293},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6413999795913696},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6057999730110168},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.5432000160217285},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5131000280380249},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.4934999942779541},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4830999970436096},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4814000129699707},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4763000011444092},{"id":"https://openalex.org/C200116569","wikidata":"https://www.wikidata.org/wiki/Q902052","display_name":"G\u00f6del's completeness theorem","level":2,"score":0.4706999957561493},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46630001068115234},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.4325000047683716},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.40799999237060547},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C1911482","wikidata":"https://www.wikidata.org/wiki/Q854531","display_name":"Real analysis","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.33500000834465027},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.32440000772476196},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.3224000036716461},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.3199000060558319},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.3124000132083893},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.28540000319480896},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2635999917984009},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2635999917984009},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3761668.3761673","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3761668.3761673","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3761668.3761673","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 17th International Conference on Computer Modeling and Simulation","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3761668.3761673","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3761668.3761673","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3761668.3761673","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 17th International Conference on Computer Modeling and Simulation","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G445591447","display_name":null,"funder_award_id":"62476028","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7113906556.pdf","grobid_xml":"https://content.openalex.org/works/W7113906556.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3215285253","https://openalex.org/W4299396019"],"related_works":[],"abstract_inverted_index":{"The":[0,58,76],"completeness":[1,179],"theorems":[2,180],"of":[3,11,19,48,86,168,204],"real":[4,49,60,91,139,169],"numbers":[5],"serve":[6],"as":[7,44],"the":[8,16,40,80,108,115,122,128,165,174,182,195,200,205],"theoretical":[9,166],"foundation":[10],"mathematical":[12,23,56,153],"analysis.":[13,32,57],"They":[14],"transform":[15],"intuitive":[17],"notion":[18],"continuity":[20,30],"into":[21],"operational":[22],"language,":[24],"providing":[25],"a":[26,89],"rigorous":[27,90],"framework":[28],"for":[29,176],"in":[31,55,64,83,137,187,194],"Among":[33],"these":[34],"theorems,":[35],"Dedekind's":[36,118],"Fundamental":[37,119],"Theorem":[38,42,120],"and":[39,121,134,158,202],"Supremum":[41,123],"stand":[43],"two":[45],"classical":[46],"formulations":[47],"number":[50,61,92,140],"completeness,":[51],"holding":[52],"fundamental":[53],"significance":[54],"formal":[59],"system":[62,77,93],"used":[63],"this":[65,104,188],"paper":[66],"is":[67],"based":[68],"entirely":[69],"on":[70,96,103],"Morse-Kelley":[71],"(MK)":[72],"axiomatic":[73],"set":[74],"theory.":[75],"strictly":[78],"follows":[79],"construction":[81],"method":[82],"Landau's":[84],"Foundations":[85],"Analysis,":[87],"establishing":[88],"without":[94],"relying":[95],"type-theoretic":[97],"foundations":[98],"or":[99],"additional":[100],"axioms.":[101],"Building":[102],"foundation,":[105],"we":[106],"employ":[107],"Coq":[109,196],"theorem":[110,197],"prover":[111],"to":[112,143],"formally":[113,192],"verify":[114],"equivalence":[116,130],"between":[117,131],"Theorem.":[124],"This":[125,160],"verification":[126],"reveals":[127],"logical":[129],"Dedekind":[132],"cuts":[133],"supremum":[135],"properties":[136],"characterizing":[138],"completeness.":[141],"Compared":[142],"type-theory-based":[144],"systems,":[145],"our":[146],"approach":[147],"aligns":[148],"more":[149],"closely":[150],"with":[151],"traditional":[152],"reasoning,":[154],"offering":[155],"better":[156],"intuitiveness":[157],"readability.":[159],"research":[161],"not":[162],"only":[163],"strengthens":[164],"basis":[167],"analysis":[170],"but":[171],"also":[172],"paves":[173],"way":[175],"formalizing":[177],"other":[178],"within":[181],"MK":[183],"framework.":[184],"All":[185],"proofs":[186],"work":[189],"have":[190],"been":[191],"verified":[193],"prover,":[198],"ensuring":[199],"rigor":[201],"reliability":[203],"reasoning":[206],"process.":[207]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-12-11T00:00:00"}
