{"id":"https://openalex.org/W1978238859","doi":"https://doi.org/10.2178/jsl/1067620175","title":"The axiom of choice and combinatory logic","display_name":"The axiom of choice and combinatory logic","publication_year":2003,"publication_date":"2003-12-01","ids":{"openalex":"https://openalex.org/W1978238859","doi":"https://doi.org/10.2178/jsl/1067620175","mag":"1978238859"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1067620175","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1067620175","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","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/A5009435902","display_name":"Andrea Cantini","orcid":null},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Andrea Cantini","raw_affiliation_strings":["Dipartimento di Filosofia, Universit\u00e0 Degli Studi di Firenze, Firenze, Italy, E-mail:","universit\u00e0 degli studi di Firenze"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Filosofia, Universit\u00e0 Degli Studi di Firenze, Firenze, Italy, E-mail:","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"universit\u00e0 degli studi di Firenze","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009435902"],"corresponding_institution_ids":["https://openalex.org/I45084792"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08700538,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"68","issue":"4","first_page":"1091","last_page":"1108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9994000196456909,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9994000196456909,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9986000061035156,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9980999827384949,"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/constructive-set-theory","display_name":"Constructive set theory","score":0.8906741142272949},{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.8779163360595703},{"id":"https://openalex.org/keywords/extensionality","display_name":"Extensionality","score":0.8568816184997559},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.8332365155220032},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.6749227643013},{"id":"https://openalex.org/keywords/combinatory-logic","display_name":"Combinatory logic","score":0.6302867531776428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6140005588531494},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6132354140281677},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5630302429199219},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.5575684309005737},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5441573262214661},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5019199848175049},{"id":"https://openalex.org/keywords/axiom-independence","display_name":"Axiom independence","score":0.5013449192047119},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.4463733434677124},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.43662533164024353},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.4104546308517456},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3903932273387909},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3710934519767761},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3293517231941223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32335278391838074},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.2927996516227722},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2897837162017822},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19234520196914673},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.16082137823104858},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.13737833499908447},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.05985754728317261}],"concepts":[{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.8906741142272949},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.8779163360595703},{"id":"https://openalex.org/C150355047","wikidata":"https://www.wikidata.org/wiki/Q965432","display_name":"Extensionality","level":2,"score":0.8568816184997559},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.8332365155220032},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.6749227643013},{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.6302867531776428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6140005588531494},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6132354140281677},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5630302429199219},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.5575684309005737},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5441573262214661},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5019199848175049},{"id":"https://openalex.org/C170088968","wikidata":"https://www.wikidata.org/wiki/Q4830547","display_name":"Axiom independence","level":3,"score":0.5013449192047119},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.4463733434677124},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.43662533164024353},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4104546308517456},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3903932273387909},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3710934519767761},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3293517231941223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32335278391838074},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.2927996516227722},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2897837162017822},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19234520196914673},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.16082137823104858},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.13737833499908447},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.05985754728317261},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2178/jsl/1067620175","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1067620175","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.412","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.412","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.disi.unige.it/aila/scuola/AC_sem02.pdf.gz","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1067620175","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1067620175","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:flore.unifi.it:2158/205053","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/205053","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W126568045","https://openalex.org/W206272296","https://openalex.org/W793849694","https://openalex.org/W1498926208","https://openalex.org/W1605406162","https://openalex.org/W1763978647","https://openalex.org/W1795577507","https://openalex.org/W1975734325","https://openalex.org/W1986998737","https://openalex.org/W2025127850","https://openalex.org/W2154273644","https://openalex.org/W2171090910","https://openalex.org/W2798718690","https://openalex.org/W2893297087","https://openalex.org/W4251260938"],"related_works":["https://openalex.org/W4233243512","https://openalex.org/W2082808755","https://openalex.org/W288388583","https://openalex.org/W1995120876","https://openalex.org/W1415587708","https://openalex.org/W4252275301","https://openalex.org/W2350176099","https://openalex.org/W2796622564","https://openalex.org/W2980408391","https://openalex.org/W2076278624"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"combine":[2],"a":[3],"variety":[4],"of":[5,27],"constructive":[6],"methods":[7],"(including":[8],"forcing,":[9],"realizability,":[10],"asymmetric":[11],"interpretation),":[12],"to":[13],"obtain":[14],"consistency":[15],"results":[16],"concerning":[17],"combinatory":[18],"logic":[19],"with":[20],"extensionality":[21],"and":[22],"(forms":[23],"of)":[24],"the":[25],"axiom":[26],"choice.":[28]},"counts_by_year":[],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}