{"id":"https://openalex.org/W2154189201","doi":"https://doi.org/10.1007/978-3-540-69407-6_52","title":"The Relative Consistency of the Axiom of Choice \u2014 Mechanized Using Isabelle/ZF","display_name":"The Relative Consistency of the Axiom of Choice \u2014 Mechanized Using Isabelle/ZF","publication_year":2008,"publication_date":"2008-06-10","ids":{"openalex":"https://openalex.org/W2154189201","doi":"https://doi.org/10.1007/978-3-540-69407-6_52","mag":"2154189201"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-69407-6_52","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-69407-6_52","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086565312","display_name":"Lawrence C. Paulson","orcid":"https://orcid.org/0000-0003-0288-4279"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Lawrence C. Paulson","raw_affiliation_strings":["Computer Laboratory, University of Cambridge, England"],"affiliations":[{"raw_affiliation_string":"Computer Laboratory, University of Cambridge, England","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086565312"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.16139918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"486","last_page":"490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9987999796867371,"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":0.9987999796867371,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9983999729156494,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7530689239501953},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.736681342124939},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6664072871208191},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6258875131607056},{"id":"https://openalex.org/keywords/contradiction","display_name":"Contradiction","score":0.5555717945098877},{"id":"https://openalex.org/keywords/assertion","display_name":"Assertion","score":0.5507069230079651},{"id":"https://openalex.org/keywords/constructive-set-theory","display_name":"Constructive set theory","score":0.5003509521484375},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.4851025342941284},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.39064064621925354},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.390169233083725},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.39003220200538635},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3797339200973511},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.37770408391952515},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3389434814453125},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2913627028465271},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25263625383377075},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.12770143151283264},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10807070136070251},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.07820284366607666}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7530689239501953},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.736681342124939},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6664072871208191},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6258875131607056},{"id":"https://openalex.org/C2776728590","wikidata":"https://www.wikidata.org/wiki/Q363948","display_name":"Contradiction","level":2,"score":0.5555717945098877},{"id":"https://openalex.org/C40422974","wikidata":"https://www.wikidata.org/wiki/Q741248","display_name":"Assertion","level":2,"score":0.5507069230079651},{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.5003509521484375},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4851025342941284},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.39064064621925354},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.390169233083725},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.39003220200538635},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3797339200973511},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.37770408391952515},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3389434814453125},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2913627028465271},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25263625383377075},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.12770143151283264},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10807070136070251},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07820284366607666},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-69407-6_52","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-69407-6_52","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1557413548","https://openalex.org/W1579218062","https://openalex.org/W1579338145","https://openalex.org/W1585415359","https://openalex.org/W1586167239","https://openalex.org/W1708264985","https://openalex.org/W1767356134","https://openalex.org/W1781706428","https://openalex.org/W1968724907","https://openalex.org/W1978413491","https://openalex.org/W1984820433","https://openalex.org/W1990347565","https://openalex.org/W1995955735","https://openalex.org/W2017971007","https://openalex.org/W2022040382","https://openalex.org/W2038389031","https://openalex.org/W2041161966","https://openalex.org/W2056145119","https://openalex.org/W2073127449","https://openalex.org/W2093397547","https://openalex.org/W2105750191","https://openalex.org/W2106721886","https://openalex.org/W2568721247"],"related_works":["https://openalex.org/W2016661762","https://openalex.org/W1574825745","https://openalex.org/W2060433450","https://openalex.org/W2079743999","https://openalex.org/W1992333765","https://openalex.org/W1587633197","https://openalex.org/W2007535202","https://openalex.org/W1538212383","https://openalex.org/W2017481539","https://openalex.org/W4243217895"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
