{"id":"https://openalex.org/W1988155600","doi":"https://doi.org/10.2307/2275651","title":"Minimal models of Heyting arithmetic","display_name":"Minimal models of Heyting arithmetic","publication_year":1997,"publication_date":"1997-12-01","ids":{"openalex":"https://openalex.org/W1988155600","doi":"https://doi.org/10.2307/2275651","mag":"1988155600"},"language":"en","primary_location":{"id":"doi:10.2307/2275651","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275651","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/A5015377052","display_name":"Ieke Moerdijk","orcid":null},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Ieke Moerdijk","raw_affiliation_strings":["Mathematical Institute, University of Utrecht, PO Box 80.010, NL-3508 TA Utrecht, The Netherlands E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Utrecht, PO Box 80.010, NL-3508 TA Utrecht, The Netherlands E-mail:","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043991180","display_name":"Erik Palmgren","orcid":"https://orcid.org/0000-0001-9830-1036"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Erik Palmgren","raw_affiliation_strings":["Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden E-mail:","institution_ids":["https://openalex.org/I123387679"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015377052"],"corresponding_institution_ids":["https://openalex.org/I193662353"],"apc_list":null,"apc_paid":null,"fwci":4.1193,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.93730039,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"62","issue":"4","first_page":"1448","last_page":"1460"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998999834060669,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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":0.9900000095367432,"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/sheaf","display_name":"Sheaf","score":0.7462233304977417},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.7135140895843506},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.704299807548523},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6419597864151001},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.5500749349594116},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.520451545715332},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5203084945678711},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.5102481842041016},{"id":"https://openalex.org/keywords/intuitionism","display_name":"Intuitionism","score":0.4956616163253784},{"id":"https://openalex.org/keywords/finitary","display_name":"Finitary","score":0.49539339542388916},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47861307859420776},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4708525538444519},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44601279497146606},{"id":"https://openalex.org/keywords/g\u00f6dels-completeness-theorem","display_name":"G\u00f6del's completeness theorem","score":0.4391135275363922},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.42017924785614014},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3204153776168823},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.30169346928596497},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2994738221168518},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.2200314998626709},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18948620557785034},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.12846243381500244},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09403243660926819}],"concepts":[{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.7462233304977417},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.7135140895843506},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.704299807548523},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6419597864151001},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.5500749349594116},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.520451545715332},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5203084945678711},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.5102481842041016},{"id":"https://openalex.org/C153107464","wikidata":"https://www.wikidata.org/wiki/Q10879018","display_name":"Intuitionism","level":2,"score":0.4956616163253784},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.49539339542388916},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47861307859420776},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4708525538444519},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44601279497146606},{"id":"https://openalex.org/C200116569","wikidata":"https://www.wikidata.org/wiki/Q902052","display_name":"G\u00f6del's completeness theorem","level":2,"score":0.4391135275363922},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.42017924785614014},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3204153776168823},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.30169346928596497},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2994738221168518},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2200314998626709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18948620557785034},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.12846243381500244},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09403243660926819},{"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2275651","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275651","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:CULeuclid:euclid.jsl/1183745390","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745390","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:repository.ubn.ru.nl:2066/129055","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/129055","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 Symbolic Logic, 62, 4, pp. 1448-1460","raw_type":"Article / Letter to editor"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W36355091","https://openalex.org/W104172771","https://openalex.org/W1601654835","https://openalex.org/W2075382666","https://openalex.org/W2078368926","https://openalex.org/W2127548353","https://openalex.org/W4251444040","https://openalex.org/W4312701703"],"related_works":["https://openalex.org/W2064301285","https://openalex.org/W2163152086","https://openalex.org/W2503573039","https://openalex.org/W2044340169","https://openalex.org/W1977645663","https://openalex.org/W2034315792","https://openalex.org/W2155188310","https://openalex.org/W2007555602","https://openalex.org/W2588547018","https://openalex.org/W4286979908"],"abstract_inverted_index":{"In":[0,121],"this":[1,122,130,145],"paper,":[2],"we":[3,124],"give":[4],"a":[5,58,111,117,126,135,162,185],"constructive":[6,59,187],"nonstandard":[7,87,197],"model":[8,29,45,102,113],"of":[9,18,43,50,73,76,86,110,119,129,138,144,153,157,180,204],"intuitionistic":[10,39,88],"arithmetic":[11,89,115],"(Heyting":[12],"arithmetic).":[13],"We":[14,191],"present":[15,125],"two":[16],"axiomatisations":[17,31,85],"the":[19,28,44,48,74,106,154,158,210],"model:":[20],"one":[21,24],"finitary":[22],"and":[23,60,94],"infinitary":[25],"variant.":[26],"Using":[27],"these":[30],"are":[32,103,200],"proven":[33],"to":[34,79,176],"be":[35,54,91,148,174],"conservative":[36],"over":[37,207],"ordinary":[38],"arithmetic.":[40],"The":[41,84,142],"definition":[42],"along":[46],"with":[47],"proofs":[49],"its":[51],"properties":[52],"may":[53],"carried":[55],"out":[56],"within":[57],"predicative":[61],"metatheory":[62],"(such":[63],"as":[64,98,100,150],"Martin-L\u00f6f's":[65],"type":[66],"theory).":[67],"This":[68],"paper":[69,123],"gives":[70],"an":[71,151],"illustration":[72],"use":[75],"sheaf":[77,112],"semantics":[78],"obtain":[80],"effective":[81],"proof-theoretic":[82],"results.":[83],"(to":[90],"called":[92],"HAI":[93,95],"\u03c9":[96],"respectively)":[97],"well":[99],"their":[101],"based":[104],"on":[105,134],"construction":[107,143,156],"in":[108,172,184],"[5]":[109],"for":[114,161,195],"using":[116],"site":[118,137,146],"filters.":[120],"\u201cminimal\u201d":[127],"version":[128],"model,":[131],"built":[132],"instead":[133],"suitable":[136],"provable":[139],"filter":[140],"bases.":[141],"can":[147,171],"viewed":[149],"extension":[152],"well-known":[155],"classifying":[159],"topos":[160],"geometric":[163],"theory":[164],"which":[165],"uses":[166],"\u201csyntactic":[167],"sites\u201d.":[168],"(Such":[169],"sites":[170],"fact":[173],"used":[175],"prove":[177],"semantical":[178],"completeness":[179],"first":[181],"order":[182],"logic":[183],"strictly":[186],"framework,":[188],"see":[189],"[6].)":[190],"should":[192],"mention":[193],"that":[194],"classical":[196],"arithmetics":[198],"there":[199],"several":[201],"nonconstructive":[202],"methods":[203],"proving":[205],"conservativity":[206],"arithmetic,":[208],"e.g.":[209],"compactness":[211],"theorem,":[212],"Mac":[213],"Dowell\u2013Specker's":[214],"theorem":[215],"[3].":[216]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-17T08:19:37.847499","created_date":"2016-06-24T00:00:00"}
