{"id":"https://openalex.org/W2800760800","doi":"https://doi.org/10.1017/s0960129518000075","title":"Realizability in ordered combinatory algebras with adjunction","display_name":"Realizability in ordered combinatory algebras with adjunction","publication_year":2018,"publication_date":"2018-04-26","ids":{"openalex":"https://openalex.org/W2800760800","doi":"https://doi.org/10.1017/s0960129518000075","mag":"2800760800"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129518000075","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129518000075","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","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/A5050651194","display_name":"Walter Ferrer Santos","orcid":null},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"WALTER FERRER SANTOS","raw_affiliation_strings":["Centro de Matem\u00e1tica, Facultad de Ciencias, Universidad de la Rep\u00fablica, Igu\u00e1 4225 11400, Montevideo, Uruguay Email:","Departamento de Matem\u00e1tica y Aplicaciones, Centro Universitario Regional del Este, Universidad de la Rep\u00fablica, Tacuaremb\u00f3 entre Avenida Artigas y Aparicio Saravia, Maldonado, Uruguay Email:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Matem\u00e1tica, Facultad de Ciencias, Universidad de la Rep\u00fablica, Igu\u00e1 4225 11400, Montevideo, Uruguay Email:","institution_ids":["https://openalex.org/I180910786"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica y Aplicaciones, Centro Universitario Regional del Este, Universidad de la Rep\u00fablica, Tacuaremb\u00f3 entre Avenida Artigas y Aparicio Saravia, Maldonado, Uruguay Email:","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085931960","display_name":"Mauricio Guillermo","orcid":null},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"MAURICIO GUILLERMO","raw_affiliation_strings":["Instituto de Matem\u00e1tica y Estad\u00edsitica Rafael Laguardia, Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, J. Herrera y Reissig 565 11300, Montevideo, Uruguay Email:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica y Estad\u00edsitica Rafael Laguardia, Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, J. Herrera y Reissig 565 11300, Montevideo, Uruguay Email:","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009974119","display_name":"Octavio Malherbe","orcid":null},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"OCTAVIO MALHERBE","raw_affiliation_strings":["Departamento de Matem\u00e1tica y Aplicaciones, Centro Universitario Regional del Este, Universidad de la Rep\u00fablica, Tacuaremb\u00f3 entre Avenida Artigas y Aparicio Saravia, Maldonado, Uruguay Email:","Instituto de Matem\u00e1tica y Estad\u00edsitica Rafael Laguardia, Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, J. Herrera y Reissig 565 11300, Montevideo, Uruguay Email:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica y Aplicaciones, Centro Universitario Regional del Este, Universidad de la Rep\u00fablica, Tacuaremb\u00f3 entre Avenida Artigas y Aparicio Saravia, Maldonado, Uruguay Email:","institution_ids":["https://openalex.org/I180910786"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica y Estad\u00edsitica Rafael Laguardia, Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, J. Herrera y Reissig 565 11300, Montevideo, Uruguay Email:","institution_ids":["https://openalex.org/I180910786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I180910786"],"apc_list":null,"apc_paid":null,"fwci":0.206,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52977658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"29","issue":"3","first_page":"430","last_page":"464"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9994000196456909,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9994000196456909,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9990000128746033,"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":0.9983000159263611,"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/adjunction","display_name":"Adjunction","score":0.9724559783935547},{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.9111838340759277},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.6942799687385559},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6859999895095825},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.562286376953125},{"id":"https://openalex.org/keywords/combinatory-logic","display_name":"Combinatory logic","score":0.5086275339126587},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5023300647735596},{"id":"https://openalex.org/keywords/closure-operator","display_name":"Closure operator","score":0.492768794298172},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.46383675932884216},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43932002782821655},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.4361320436000824},{"id":"https://openalex.org/keywords/composability","display_name":"Composability","score":0.4215278923511505},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3283083736896515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2761419415473938},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15046349167823792},{"id":"https://openalex.org/keywords/closed-set","display_name":"Closed set","score":0.15038838982582092}],"concepts":[{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.9724559783935547},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.9111838340759277},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.6942799687385559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6859999895095825},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.562286376953125},{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.5086275339126587},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5023300647735596},{"id":"https://openalex.org/C160771489","wikidata":"https://www.wikidata.org/wiki/Q10564851","display_name":"Closure operator","level":3,"score":0.492768794298172},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.46383675932884216},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43932002782821655},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.4361320436000824},{"id":"https://openalex.org/C2778814252","wikidata":"https://www.wikidata.org/wiki/Q5156715","display_name":"Composability","level":2,"score":0.4215278923511505},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3283083736896515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2761419415473938},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15046349167823792},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.15038838982582092},{"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/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0960129518000075","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129518000075","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W45266662","https://openalex.org/W624912723","https://openalex.org/W1942966263","https://openalex.org/W1971613396","https://openalex.org/W1990564510","https://openalex.org/W2056300881","https://openalex.org/W2091708223","https://openalex.org/W2096877663","https://openalex.org/W2118238767","https://openalex.org/W2126988924","https://openalex.org/W2135287414","https://openalex.org/W2291208220","https://openalex.org/W2574983198","https://openalex.org/W2963271462","https://openalex.org/W3098060485","https://openalex.org/W3098832446","https://openalex.org/W4243933121","https://openalex.org/W4298280132"],"related_works":["https://openalex.org/W2779380694","https://openalex.org/W2302431466","https://openalex.org/W4296293112","https://openalex.org/W1869822899","https://openalex.org/W2518030588","https://openalex.org/W4300620218","https://openalex.org/W2158838886","https://openalex.org/W4233763932","https://openalex.org/W1574045147","https://openalex.org/W1561592828"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,74],"continue":[4],"our":[5,116],"consideration":[6],"of":[7,31,35,40,54,63,70,83,86],"the":[8,12,25,29,32,41,52,55,60,64,68,81,84,96,106,126,132,142,149,162],"constructions":[9,107],"presented":[10,114],"in":[11,115,125],"paper":[13,49],"Krivine's":[14],"Classical":[15],"Realizability":[16],"from":[17,108],"a":[18,71,76],"Categorical":[19],"Perspective":[20],"by":[21,45,67,139],"Thomas":[22],"Streicher.":[23],"Therein,":[24],"author":[26],"points":[27],"towards":[28],"interpretation":[30],"classical":[33],"realizability":[34],"Krivine":[36,89,159],"as":[37,161],"an":[38,87,93],"instance":[39],"categorical":[42,61],"approach":[43],"started":[44],"Hyland.":[46],"The":[47],"present":[48],"continues":[50],"with":[51,153],"study":[53],"basic":[56,163],"algebraic":[57],"set-up":[58],"underlying":[59],"aspects":[62],"theory.":[65],"Motivated":[66],"search":[69],"full":[72,154],"adjunction,":[73],"introduce":[75],"new":[77,127],"closure":[78],"operator":[79],"on":[80],"subsets":[82],"stacks":[85],"abstract":[88,158],"structure":[90],"that":[91,104,130,141],"yields":[92],"adjunction":[94,155],"between":[95],"corresponding":[97],"application":[98],"and":[99,129],"implication":[100],"operations.":[101],"We":[102,137],"show":[103],"all":[105,131],"ordered":[109,150],"combinatory":[110,151],"algebras":[111,152],"to":[112],"triposes":[113,134],"previous":[117],"work":[118],"can":[119,145],"be":[120,146],"implemented,":[121],"mutatis":[122],"mutandis":[123],",":[124],"situation":[128],"associated":[133],"are":[135],"equivalent.":[136],"finish":[138],"proving":[140],"whole":[143],"theory":[144],"developed":[147],"using":[148],"or":[156],"strong":[157],"structures":[160],"set-up.":[164]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}