{"id":"https://openalex.org/W2079355284","doi":"https://doi.org/10.1142/s0219061314500056","title":"The axiom of multiple choice and models for constructive set theory","display_name":"The axiom of multiple choice and models for constructive set theory","publication_year":2014,"publication_date":"2014-03-28","ids":{"openalex":"https://openalex.org/W2079355284","doi":"https://doi.org/10.1142/s0219061314500056","mag":"2079355284"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061314500056","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061314500056","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://handle.uba.uva.nl/personal/pure/en/publications/the-axiom-of-multiple-choice-and-models-for-constructive-set-theory(879228a3-cc90-4771-9f58-f0c4b50fbb8e).html","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040167167","display_name":"Benno van den Berg","orcid":"https://orcid.org/0000-0002-0469-0788"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Benno van den Berg","raw_affiliation_strings":["ILLC, Universiteit van Amsterdam, P.O. Box 94242, 1090 GE Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"ILLC, Universiteit van Amsterdam, P.O. Box 94242, 1090 GE Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015377052","display_name":"Ieke Moerdijk","orcid":null},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ieke Moerdijk","raw_affiliation_strings":["Institute for Mathematics, Astrophysics, and Particle Physics, Radboud Universiteit Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, Astrophysics, and Particle Physics, Radboud Universiteit Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040167167"],"corresponding_institution_ids":["https://openalex.org/I887064364"],"apc_list":null,"apc_paid":null,"fwci":2.2901,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.8715237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"01","first_page":"1450005","last_page":"1450005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9860000014305115,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9821000099182129,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/constructive-set-theory","display_name":"Constructive set theory","score":0.8467408418655396},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.8358038067817688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8179173469543457},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.6380066275596619},{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.6143009066581726},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5996032953262329},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5923716425895691},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5922578573226929},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.5894627571105957},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5785098075866699},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5398982763290405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48873043060302734},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.4449806809425354},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39789682626724243},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.38612082600593567},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3642445206642151},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.2215850055217743},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12672096490859985},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11298713088035583}],"concepts":[{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.8467408418655396},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.8358038067817688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8179173469543457},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.6380066275596619},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.6143009066581726},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5996032953262329},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5923716425895691},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5922578573226929},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.5894627571105957},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5785098075866699},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5398982763290405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48873043060302734},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.4449806809425354},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39789682626724243},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.38612082600593567},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3642445206642151},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2215850055217743},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12672096490859985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11298713088035583},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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":6,"locations":[{"id":"doi:10.1142/s0219061314500056","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061314500056","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:dare.uva.nl:openaire/879228a3-cc90-4771-9f58-f0c4b50fbb8e","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/the-axiom-of-multiple-choice-and-models-for-constructive-set-theory(879228a3-cc90-4771-9f58-f0c4b50fbb8e).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"van den Berg, B & Moerdijk, I 2014, 'The axiom of multiple choice and models for constructive set theory', Journal of Mathematical Logic, vol. 14, no. 1, 1450005. https://doi.org/10.1142/S0219061314500056","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/879228a3-cc90-4771-9f58-f0c4b50fbb8e","is_oa":true,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/the-axiom-of-multiple-choice-and-models-for-constructive-set-theory(879228a3-cc90-4771-9f58-f0c4b50fbb8e).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"van den Berg, B & Moerdijk, I 2014, 'The axiom of multiple choice and models for constructive set theory', Journal of Mathematical Logic, vol. 14, no. 1, 1450005. https://doi.org/10.1142/S0219061314500056","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1204.4045","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.4045","pdf_url":"https://arxiv.org/pdf/1204.4045","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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:dare.uva.nl:publications/879228a3-cc90-4771-9f58-f0c4b50fbb8e","is_oa":false,"landing_page_url":"https://arxiv.org/abs/1204.4045","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:repository.ubn.ru.nl:2066/130240","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/130240","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Logic, 14, 1, pp. 1450005(1)-1450005(28)","raw_type":"Article / Letter to editor"}],"best_oa_location":{"id":"pmh:oai:dare.uva.nl:openaire/879228a3-cc90-4771-9f58-f0c4b50fbb8e","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/the-axiom-of-multiple-choice-and-models-for-constructive-set-theory(879228a3-cc90-4771-9f58-f0c4b50fbb8e).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"van den Berg, B & Moerdijk, I 2014, 'The axiom of multiple choice and models for constructive set theory', Journal of Mathematical Logic, vol. 14, no. 1, 1450005. https://doi.org/10.1142/S0219061314500056","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W77027564","https://openalex.org/W1498439614","https://openalex.org/W1589408343","https://openalex.org/W1786644787","https://openalex.org/W1983905931","https://openalex.org/W1992333765","https://openalex.org/W2060996059","https://openalex.org/W2121213425","https://openalex.org/W2122521516","https://openalex.org/W2143931279","https://openalex.org/W2152342937","https://openalex.org/W2163641933","https://openalex.org/W2601545920","https://openalex.org/W3099209700","https://openalex.org/W6833449961"],"related_works":["https://openalex.org/W4233243512","https://openalex.org/W2350176099","https://openalex.org/W288388583","https://openalex.org/W423103167","https://openalex.org/W102859336","https://openalex.org/W1541896744","https://openalex.org/W3034881686","https://openalex.org/W2114683125","https://openalex.org/W2031083694","https://openalex.org/W2055120637"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2,11],"extension":[3,24,108,135],"of":[4,65],"Aczel's":[5],"constructive":[6,40],"set":[7,78,152],"theory":[8,35,153],"CZF":[9],"by":[10,146],"axiom":[12],"for":[13,119,127],"inductive":[14],"types":[15],"and":[16,20,41,56,122],"a":[17,39,94,115,123],"choice":[18],"principle,":[19],"show":[21,105,132],"that":[22,106,133,141],"this":[23,66,107,134],"has":[25],"the":[26,52,57,73,139,147],"following":[27],"properties:":[28],"it":[29,46,69,142],"is":[30,47,70,136,143],"interpretable":[31],"in":[32,59,138],"Martin-L\u00f6f's":[33],"type":[34],"(hence":[36],"acceptable":[37],"from":[38,76,97,150],"generalized-predicative":[42],"standpoint).":[43],"In":[44],"addition,":[45],"strong":[48],"enough":[49],"to":[50,104],"prove":[51],"Set":[53],"Compactness":[54],"theorem":[55],"results":[58],"formal":[60],"topology":[61],"which":[62],"make":[63],"use":[64],"theorem.":[67],"Moreover,":[68],"stable":[71],"under":[72],"standard":[74],"constructions":[75,149],"algebraic":[77,151],"theory,":[79],"namely":[80],"exact":[81],"completion,":[82],"realizability":[83],"models,":[84],"forcing":[85],"as":[86,88,114],"well":[87],"more":[89],"general":[90],"sheaf":[91],"extensions.":[92],"As":[93],"result,":[95],"methods":[96],"our":[98],"earlier":[99],"work":[100],"can":[101],"be":[102],"applied":[103],"satisfies":[109],"various":[110],"derived":[111,116,124],"rules,":[112],"such":[113],"compactness":[117],"rule":[118,126],"Cantor":[120],"space":[121],"continuity":[125],"Baire":[128],"space.":[129],"Finally,":[130],"we":[131],"robust":[137],"sense":[140],"also":[144],"reflected":[145],"model":[148],"just":[154],"mentioned.":[155]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}