{"id":"https://openalex.org/W3138716284","doi":"https://doi.org/10.1007/978-3-030-71995-1_1","title":"Constructing a universe for the setoid model","display_name":"Constructing a universe for the setoid model","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3138716284","doi":"https://doi.org/10.1007/978-3-030-71995-1_1","mag":"3138716284"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-71995-1_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-71995-1_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-71995-1_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-71995-1_1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056420469","display_name":"Thorsten Altenkirch","orcid":"https://orcid.org/0000-0002-6582-5025"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Thorsten Altenkirch","raw_affiliation_strings":["School of Computer Science, University of Nottingham, Nottingham, UK"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Nottingham, Nottingham, UK","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024829251","display_name":"Simon Boulier","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Simon Boulier","raw_affiliation_strings":["Inria, Nantes, France"],"affiliations":[{"raw_affiliation_string":"Inria, Nantes, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047340010","display_name":"Ambrus Kaposi","orcid":"https://orcid.org/0000-0001-9897-8936"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Ambrus Kaposi","raw_affiliation_strings":["E\u00f6tv\u00f6s Lor\u00e1nd University, Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"E\u00f6tv\u00f6s Lor\u00e1nd University, Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103055014","display_name":"Christian Sattler","orcid":"https://orcid.org/0000-0001-6374-4427"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Christian Sattler","raw_affiliation_strings":["Chalmers University of Technology, Gothenburg, Sweden"],"affiliations":[{"raw_affiliation_string":"Chalmers University of Technology, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081750865","display_name":"Filippo Sestini","orcid":"https://orcid.org/0000-0002-8701-5613"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Filippo Sestini","raw_affiliation_strings":["School of Computer Science, University of Nottingham, Nottingham, UK"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Nottingham, Nottingham, UK","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5056420469"],"corresponding_institution_ids":["https://openalex.org/I142263535"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.7172,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6792123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9950000047683716,"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":0.9950000047683716,"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":0.9855999946594238,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9810000061988831,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/extensionality","display_name":"Extensionality","score":0.9936971664428711},{"id":"https://openalex.org/keywords/metatheory","display_name":"Metatheory","score":0.8475993871688843},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.8244056105613708},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6325632333755493},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6253350973129272},{"id":"https://openalex.org/keywords/universe","display_name":"Universe","score":0.44799911975860596},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4350741505622864},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4048580527305603},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2854859232902527},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2701256275177002},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.24746721982955933},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06520763039588928}],"concepts":[{"id":"https://openalex.org/C150355047","wikidata":"https://www.wikidata.org/wiki/Q965432","display_name":"Extensionality","level":2,"score":0.9936971664428711},{"id":"https://openalex.org/C39387531","wikidata":"https://www.wikidata.org/wiki/Q1096708","display_name":"Metatheory","level":2,"score":0.8475993871688843},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.8244056105613708},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6325632333755493},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6253350973129272},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.44799911975860596},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4350741505622864},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4048580527305603},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2854859232902527},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2701256275177002},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.24746721982955933},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06520763039588928},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/978-3-030-71995-1_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-71995-1_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-71995-1_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:nottingham-repository.worktribe.com:5421642","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/5421642","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:edit.elte.hu:10831/110544","is_oa":true,"landing_page_url":"http://hdl.handle.net/10831/110544","pdf_url":"https://edit.elte.hu/xmlui/bitstream/10831/110544/1/31936961.pdf","source":{"id":"https://openalex.org/S4306400126","display_name":"ELTE Digital Institutional Repository (EDIT) (E\u00f6tv\u00f6s Lor\u00e1nd University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I106118109","host_organization_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","host_organization_lineage":["https://openalex.org/I106118109"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pubmedcentral.nih.gov:7984117","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7984117","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Foundations of Software Science and Computation Structures","raw_type":"Text"},{"id":"pmh:oai:research.chalmers.se:524826","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/524826","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1007/978-3-030-71995-1_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-71995-1_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-71995-1_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1361938442","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1783795302","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G2744728761","display_name":null,"funder_award_id":"TKP2020","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"},{"id":"https://openalex.org/G3988409770","display_name":null,"funder_award_id":"TKP2020-NKA-06","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G4627546747","display_name":null,"funder_award_id":"P2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6752174271","display_name":null,"funder_award_id":"FA9550-16-1-0029","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G6869543050","display_name":null,"funder_award_id":"637339","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7090116110","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G7487386128","display_name":null,"funder_award_id":"EP/M016994/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7541558665","display_name":null,"funder_award_id":"Bolyai","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G7819609808","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G8036280063","display_name":null,"funder_award_id":"TKP2020-NKA-06","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8080935424","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G8348896211","display_name":null,"funder_award_id":"Bolyai Fellowship","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G8452545418","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322192","display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","ror":"https://ror.org/02ks8qq67"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320322663","display_name":"Universiteit Stellenbosch","ror":"https://ror.org/05bk57929"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320335908","display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap","ror":null},{"id":"https://openalex.org/F4320338112","display_name":"Exploratory Research for Advanced Technology","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3138716284.pdf","grobid_xml":"https://content.openalex.org/works/W3138716284.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1494555245","https://openalex.org/W1498439614","https://openalex.org/W1539303361","https://openalex.org/W1773829243","https://openalex.org/W1821509023","https://openalex.org/W2058174669","https://openalex.org/W2111690589","https://openalex.org/W2116438866","https://openalex.org/W2133629640","https://openalex.org/W2148713425","https://openalex.org/W2151159855","https://openalex.org/W2151520617","https://openalex.org/W2274485505","https://openalex.org/W2395623455","https://openalex.org/W2550513301","https://openalex.org/W2888153140","https://openalex.org/W2901304827","https://openalex.org/W2963795353","https://openalex.org/W2971463921","https://openalex.org/W2972845810","https://openalex.org/W2991183811","https://openalex.org/W3088552701","https://openalex.org/W3105059835","https://openalex.org/W3138202147","https://openalex.org/W4205572415"],"related_works":["https://openalex.org/W2964029175","https://openalex.org/W2787765784","https://openalex.org/W4299576734","https://openalex.org/W2963775463","https://openalex.org/W2432956223","https://openalex.org/W4205724670","https://openalex.org/W2557961224","https://openalex.org/W4297623348","https://openalex.org/W3138716284","https://openalex.org/W3188022539"],"abstract_inverted_index":{"Abstract":[0],"The":[1,35,61],"setoid":[2,62,100,149],"model":[3,6,39,63],"is":[4,41,78,157],"a":[5,25,48,56,69,104,113,130,142,189,195,200],"of":[7,28,37,81,119,132,141,145],"intensional":[8,82],"type":[9,51,84,120,198],"theory":[10,85,106],"that":[11,30,42,88,96,181],"validates":[12],"certain":[13],"extensionality":[14,18,94],"principles,":[15],"like":[16],"function":[17],"and":[19,164],"propositional":[20],"extensionality,":[21],"the":[22,93,99,117,139,148],"latter":[23],"being":[24],"limited":[26],"form":[27],"univalence":[29],"equates":[31],"logically":[32],"equivalent":[33],"propositions.":[34],"appeal":[36],"this":[38,135],"construction":[40,140,183],"it":[43],"can":[44,184],"be":[45,186],"constructed":[46],"in":[47,98,188],"small,":[49],"intensional,":[50],"theoretic":[52],"metatheory,":[53],"therefore":[54],"giving":[55],"method":[57],"to":[58,92,115,126,160,166,177],"boostrap":[59],"extensionality.":[60],"has":[64],"been":[65],"recently":[66],"adapted":[67],"into":[68],"formal":[70],"system,":[71],"namely":[72],"Setoid":[73],"Type":[74],"Theory":[75],"(SeTT).":[76],"SeTT":[77,110,128],"an":[79,153,161,167],"extension":[80],"Martin-L\u00f6f":[83],"with":[86,129,199],"constructs":[87],"give":[89],"full":[90],"access":[91],"principles":[95],"hold":[97],"model.":[101],"Although":[102],"already":[103],"rich":[105],"as":[107,152],"currently":[108,111],"defined,":[109],"lacks":[112],"way":[114],"internalize":[116],"notion":[118],"beyond":[121],"propositions,":[122],"hence":[123],"we":[124,137],"want":[125],"extend":[127],"universe":[131,144],"setoids.":[133],"To":[134],"aim,":[136],"present":[138],"(non-univalent)":[143],"setoids":[146],"within":[147],"model,":[150],"first":[151],"inductive-recursive":[154],"definition,":[155],"which":[156,193],"then":[158],"translated":[159],"inductive-inductive":[162],"definition":[163,175],"finally":[165],"inductive":[168],"family.":[169],"These":[170],"translations":[171],"from":[172],"more":[173],"powerful":[174],"schemas":[176],"simpler":[178],"ones":[179],"ensure":[180],"our":[182],"still":[185],"defined":[187],"relatively":[190],"small":[191],"metatheory":[192],"includes":[194],"proof-irrelevant":[196],"identity":[197],"strong":[201],"transport":[202],"rule.":[203]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}