{"id":"https://openalex.org/W7154314897","doi":"https://doi.org/10.1017/s0960129526100528","title":"Effectiveness and continuity in intuitionistic quasi-toposes of assemblies","display_name":"Effectiveness and continuity in intuitionistic quasi-toposes of assemblies","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7154314897","doi":"https://doi.org/10.1017/s0960129526100528"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129526100528","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129526100528","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C8A43E59CD4FD8B4C51E3675E74BC44D/S0960129526100528a.pdf/div-class-title-effectiveness-and-continuity-in-intuitionistic-quasi-toposes-of-assemblies-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C8A43E59CD4FD8B4C51E3675E74BC44D/S0960129526100528a.pdf/div-class-title-effectiveness-and-continuity-in-intuitionistic-quasi-toposes-of-assemblies-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053199287","display_name":"Maria Emilia Maietti","orcid":"https://orcid.org/0000-0002-9198-066X"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Maria Emilia Maietti","raw_affiliation_strings":["Universit\u00e0 degli Studi di Padova"],"raw_orcid":"https://orcid.org/0000-0002-9198-066X","affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Padova","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049504979","display_name":"Pietro Sabelli","orcid":"https://orcid.org/0009-0009-5050-1915"},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"government","lineage":["https://openalex.org/I202391551"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Pietro Sabelli","raw_affiliation_strings":["Czech Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Czech Academy of Sciences","institution_ids":["https://openalex.org/I202391551"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074259281","display_name":"Davide Trotta","orcid":"https://orcid.org/0000-0003-4509-594X"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Davide Trotta","raw_affiliation_strings":["Universit\u00e0 degli Studi di Padova"],"raw_orcid":"https://orcid.org/0000-0003-4509-594X","affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Padova","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053199287"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.42390812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.5450999736785889,"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/T10126","display_name":"Logic, programming, and type systems","score":0.5450999736785889,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.33009999990463257,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.03920000046491623,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.8474000096321106},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.7440000176429749},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6367999911308289},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5013999938964844},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.49050000309944153},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.48429998755455017},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46869999170303345},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.4180999994277954}],"concepts":[{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.8474000096321106},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.7440000176429749},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6367999911308289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6274999976158142},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5013999938964844},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.49050000309944153},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.48429998755455017},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46869999170303345},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.4180999994277954},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.40720000863075256},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3889000117778778},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33709999918937683},{"id":"https://openalex.org/C72727785","wikidata":"https://www.wikidata.org/wiki/Q2518298","display_name":"Category of sets","level":3,"score":0.32850000262260437},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.27950000762939453},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2768000066280365},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26100000739097595},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0960129526100528","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129526100528","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C8A43E59CD4FD8B4C51E3675E74BC44D/S0960129526100528a.pdf/div-class-title-effectiveness-and-continuity-in-intuitionistic-quasi-toposes-of-assemblies-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/s0960129526100528","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129526100528","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C8A43E59CD4FD8B4C51E3675E74BC44D/S0960129526100528a.pdf/div-class-title-effectiveness-and-continuity-in-intuitionistic-quasi-toposes-of-assemblies-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2849476320","display_name":null,"funder_award_id":"LQ300092101","funder_id":"https://openalex.org/F4320322482","funder_display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320322482","display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky","ror":"https://ror.org/053avzc18"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7154314897.pdf","grobid_xml":"https://content.openalex.org/works/W7154314897.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W141536115","https://openalex.org/W240725829","https://openalex.org/W1486536800","https://openalex.org/W1590304156","https://openalex.org/W1919166405","https://openalex.org/W1966374748","https://openalex.org/W1980497153","https://openalex.org/W1982721516","https://openalex.org/W1986402635","https://openalex.org/W1996443480","https://openalex.org/W2005065769","https://openalex.org/W2006709633","https://openalex.org/W2065468423","https://openalex.org/W2078095689","https://openalex.org/W2082627770","https://openalex.org/W2082631236","https://openalex.org/W2085205555","https://openalex.org/W2085254659","https://openalex.org/W2107996244","https://openalex.org/W2119717000","https://openalex.org/W2120677003","https://openalex.org/W2166869969","https://openalex.org/W2168025539","https://openalex.org/W2291208220","https://openalex.org/W2768904695","https://openalex.org/W4233061514","https://openalex.org/W4235960492","https://openalex.org/W4255868951","https://openalex.org/W4388321602","https://openalex.org/W4403457932","https://openalex.org/W4413965752"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,28,92,122,171,188],"well":[3],"known":[4],"that":[5,21,81,152,169,184,207],"over":[6],"Heyting":[7],"arithmetic":[8,46],"with":[9,30,112,142,218],"finite":[10],"types,":[11],"the":[12,16,35,39,50,57,62,72,85,96,130,139,161,174,185,194,197,203,213],"effective":[13,103,214],"principle":[14,215],"of":[15,68,84,98,196,199],"formal":[17],"Church":[18,74],"thesis,":[19],"stating":[20],"all":[22,82],"number-theoretic":[23],"functional":[24],"relations":[25],"are":[26,88,156],"computable,":[27],"inconsistent":[29],"Brouwer\u2019s":[31,53,113,219],"intuitionistic":[32,106,132],"principles":[33,115,221],"on":[34,49,61,202],"continuum,":[36],"in":[37,129,135,190],"particular,":[38],"fan":[40],"theorem.":[41],"Here,":[42],"we":[43,167],"build":[44],"two":[45,154],"quasi-toposes,":[47],"validating":[48],"one":[51],"hand":[52],"continuity":[54,114,220],"principles,":[55],"including":[56],"Fan":[58],"theorem,":[59],"and":[60,76,145,206],"other":[63,120],"hand,":[64],"a":[65],"restricted":[66],"form":[67],"Church\u2019s":[69],"Thesis,":[70],"called":[71],"Type-theoretic":[73],"Thesis":[75],"written":[77],"$\\textsf{TCT}$":[78,216],",":[79],"expressing":[80],"morphisms":[83],"considered":[86],"quasi-topos":[87,91,121],"computable.":[89],"One":[90],"constructed":[93],"by":[94,138,193],"formalizing":[95],"category":[97],"assemblies":[99],"$\\mathbf{Asm}$":[100],"within":[101,160,178],"Hyland\u2019s":[102],"topos":[104,210],"using":[105],"Zermelo-Fraenkel":[107],"set":[108,164],"theory":[109],"$\\mathbf{IZF}$":[110,179],"extended":[111],"as":[116,124],"our":[117],"meta-theory.":[118,133],"The":[119],"obtained":[123],"an":[125],"elementary":[126],"quotient":[127],"completion":[128],"same":[131],"While":[134],"previous":[136],"work":[137],"first":[140],"author":[141],"F.":[143],"Pasquali":[144],"G.":[146],"Rosolini,":[147],"it":[148],"has":[149],"been":[150],"shown":[151],"these":[153],"quasi-toposes":[155,192],"equivalent":[157],"when":[158,176],"working":[159,177],"classical":[162],"$\\mathbf{ZFC}$":[163],"theory;":[165],"here,":[166],"show":[168],"this":[170],"no":[172,208],"longer":[173],"case":[175],".":[180],"We":[181],"also":[182],"observe":[183],"aforementioned":[186],"inconsistency":[187],"resolved":[189],"such":[191],"non-validity":[195],"axiom":[198],"unique":[200],"choice":[201],"natural":[204],"numbers":[205],"non-trivial":[209],"can":[211],"validate":[212],"together":[217],"altogether.":[222]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-04-15T00:00:00"}
