{"id":"https://openalex.org/W2071971451","doi":"https://doi.org/10.1002/malq.19920380118","title":"AN INTERPRETATION OF MARTIN\u2010L\u00d6F'S CONSTRUCTIVE THEORY OF TYPES IN ELEMENTARY TOPOS THEORY","display_name":"AN INTERPRETATION OF MARTIN\u2010L\u00d6F'S CONSTRUCTIVE THEORY OF TYPES IN ELEMENTARY TOPOS THEORY","publication_year":1992,"publication_date":"1992-01-01","ids":{"openalex":"https://openalex.org/W2071971451","doi":"https://doi.org/10.1002/malq.19920380118","mag":"2071971451"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19920380118","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19920380118","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5079203732","display_name":"Anne Preller","orcid":null},"institutions":[{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Anne Preller","raw_affiliation_strings":["Centre de Recherche et Informatique de Montpellier 860, rue de Saint Priest F-34100 Montpellier France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre de Recherche et Informatique de Montpellier 860, rue de Saint Priest F-34100 Montpellier France","institution_ids":["https://openalex.org/I4210115519"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079203732"],"corresponding_institution_ids":["https://openalex.org/I4210115519"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.21647002,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"1","first_page":"213","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9715999960899353,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9715999960899353,"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/T10799","display_name":"Data Visualization and Analytics","score":0.9502000212669373,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/topos-theory","display_name":"Topos theory","score":0.9008665084838867},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.8605290651321411},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.783738374710083},{"id":"https://openalex.org/keywords/pullback","display_name":"Pullback","score":0.7708197832107544},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.571444571018219},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.555800199508667},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.5516130924224854},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5148112177848816},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5038778185844421},{"id":"https://openalex.org/keywords/arrow","display_name":"Arrow","score":0.45682764053344727},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.4499283730983734},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33680230379104614},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.14603084325790405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09467798471450806},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.08273965120315552}],"concepts":[{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.9008665084838867},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.8605290651321411},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.783738374710083},{"id":"https://openalex.org/C2777680557","wikidata":"https://www.wikidata.org/wiki/Q7259417","display_name":"Pullback","level":2,"score":0.7708197832107544},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.571444571018219},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.555800199508667},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.5516130924224854},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5148112177848816},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5038778185844421},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.45682764053344727},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.4499283730983734},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33680230379104614},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.14603084325790405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09467798471450806},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.08273965120315552},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":1,"locations":[{"id":"doi:10.1002/malq.19920380118","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19920380118","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W569543113","https://openalex.org/W2006941708","https://openalex.org/W2022837260","https://openalex.org/W2106718208","https://openalex.org/W2124798629","https://openalex.org/W2139794864","https://openalex.org/W2158473287","https://openalex.org/W4233299548","https://openalex.org/W4248915083"],"related_works":["https://openalex.org/W4293877434","https://openalex.org/W4235457803","https://openalex.org/W2954155107","https://openalex.org/W2556917400","https://openalex.org/W4388254072","https://openalex.org/W2614930862","https://openalex.org/W4247856587","https://openalex.org/W2905232526","https://openalex.org/W4226410745","https://openalex.org/W2789755614"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"give":[2],"a":[3,20,71],"formal":[4],"interpretation":[5,69,88],"of":[6,10,26,37,48,59,70,79,92],"Martin\u2010L\u00f6f's":[7],"Constructive":[8],"Theory":[9,15],"Types":[11,28],"in":[12],"Elementary":[13],"Topos":[14],"which":[16,65],"is":[17,41,73],"presented":[18],"as":[19,31,35],"formalised":[21],"theory":[22],"with":[23],"intensional":[24,55,74],"equality":[25,56,58],"objects.":[27],"are":[29],"interpreted":[30],"arrows":[32],"and":[33],"variables":[34],"sections":[36],"their":[38],"types.":[39,60,93],"This":[40],"necessary":[42],"to":[43,76,89],"model":[44],"correctly":[45],"the":[46,49,68,77],"working":[47],"assumption":[50],"x":[51],"\u2208":[52],"A.":[53],"Then":[54],"interprets":[57],"The":[61],"normal":[62],"form":[63],"theorem":[64],"asserts":[66],"that":[67],"type":[72],"equal":[75],"pullback":[78],"its":[80],"\u201calignment\u201d":[81],"along":[82],"some":[83],"\u201cbase\u201d":[84],"arrow":[85],"relates":[86],"this":[87],"categorical":[90],"semantic":[91]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
