{"id":"https://openalex.org/W4382628855","doi":"https://doi.org/10.1093/logcom/exad022","title":"The extended predicative Mahlo universe in Martin-L\u00f6f type theory","display_name":"The extended predicative Mahlo universe in Martin-L\u00f6f type theory","publication_year":2023,"publication_date":"2023-05-12","ids":{"openalex":"https://openalex.org/W4382628855","doi":"https://doi.org/10.1093/logcom/exad022"},"language":"en","primary_location":{"id":"doi:10.1093/logcom/exad022","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1093/logcom/exad022","pdf_url":"https://academic.oup.com/logcom/advance-article-pdf/doi/10.1093/logcom/exad022/50288571/exad022.pdf","source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://academic.oup.com/logcom/advance-article-pdf/doi/10.1093/logcom/exad022/50288571/exad022.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053761104","display_name":"Peter Dybjer","orcid":"https://orcid.org/0000-0003-4043-5204"},"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":true,"raw_author_name":"Peter Dybjer","raw_affiliation_strings":["Department of Computer Science and Engineering , Chalmers University of Technology, Gothenburg, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering , Chalmers University of Technology, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060337321","display_name":"Anton Setzer","orcid":"https://orcid.org/0000-0001-5322-6060"},"institutions":[{"id":"https://openalex.org/I39586589","display_name":"Swansea University","ror":"https://ror.org/053fq8t95","country_code":"GB","type":"education","lineage":["https://openalex.org/I39586589"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Anton Setzer","raw_affiliation_strings":["Department of Computer Science , Swansea University, Swansea, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Swansea University, Swansea, UK","institution_ids":["https://openalex.org/I39586589"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053761104"],"corresponding_institution_ids":["https://openalex.org/I66862912"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":{"value":4151,"currency":"USD","value_usd":4151},"fwci":0.1777,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54641667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"34","issue":"6","first_page":"1032","last_page":"1063"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9979000091552734,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9945999979972839,"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/predicative-expression","display_name":"Predicative expression","score":0.9859932661056519},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.7993322014808655},{"id":"https://openalex.org/keywords/universe","display_name":"Universe","score":0.6271200180053711},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5841729640960693},{"id":"https://openalex.org/keywords/dependent-type","display_name":"Dependent type","score":0.5349951982498169},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4535438120365143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4212481677532196},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3499099016189575},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3381202518939972},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33095037937164307},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2317621111869812},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.203994482755661},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.13286620378494263},{"id":"https://openalex.org/keywords/lambda-calculus","display_name":"Lambda calculus","score":0.11327022314071655}],"concepts":[{"id":"https://openalex.org/C129131279","wikidata":"https://www.wikidata.org/wiki/Q1931259","display_name":"Predicative expression","level":2,"score":0.9859932661056519},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.7993322014808655},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.6271200180053711},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5841729640960693},{"id":"https://openalex.org/C20528804","wikidata":"https://www.wikidata.org/wiki/Q997433","display_name":"Dependent type","level":3,"score":0.5349951982498169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4535438120365143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4212481677532196},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3499099016189575},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3381202518939972},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33095037937164307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2317621111869812},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.203994482755661},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.13286620378494263},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.11327022314071655},{"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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1093/logcom/exad022","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1093/logcom/exad022","pdf_url":"https://academic.oup.com/logcom/advance-article-pdf/doi/10.1093/logcom/exad022/50288571/exad022.pdf","source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},{"id":"pmh:oai:research.chalmers.se:536011","is_oa":true,"landing_page_url":"https://research.chalmers.se/en/publication/536011","pdf_url":"https://research.chalmers.se/publication/536011/file/536011_Fulltext.pdf","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":""},{"id":"pmh:oai:cronfa.swan.ac.uk:cronfa63064","is_oa":true,"landing_page_url":"https://cronfa.swan.ac.uk/Record/cronfa63064","pdf_url":null,"source":{"id":"https://openalex.org/S4306401612","display_name":"Cronfa (Swansea University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39586589","host_organization_name":"Swansea University","host_organization_lineage":["https://openalex.org/I39586589"],"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":null,"raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.1093/logcom/exad022","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1093/logcom/exad022","pdf_url":"https://academic.oup.com/logcom/advance-article-pdf/doi/10.1093/logcom/exad022/50288571/exad022.pdf","source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382628855.pdf","grobid_xml":"https://content.openalex.org/works/W4382628855.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W126568045","https://openalex.org/W159354440","https://openalex.org/W569543113","https://openalex.org/W1518280455","https://openalex.org/W1539303361","https://openalex.org/W1593841126","https://openalex.org/W1763978647","https://openalex.org/W1968916436","https://openalex.org/W1973691337","https://openalex.org/W2015181892","https://openalex.org/W2043354427","https://openalex.org/W2058174669","https://openalex.org/W2064023341","https://openalex.org/W2074842064","https://openalex.org/W2088156780","https://openalex.org/W2096744225","https://openalex.org/W2116942026","https://openalex.org/W2120826243","https://openalex.org/W2124798629","https://openalex.org/W2132221175","https://openalex.org/W2151520617","https://openalex.org/W2229616979","https://openalex.org/W2552040597","https://openalex.org/W2608797165","https://openalex.org/W3104826616","https://openalex.org/W6688469203"],"related_works":["https://openalex.org/W3022980401","https://openalex.org/W2152655108","https://openalex.org/W4295295521","https://openalex.org/W2143617699","https://openalex.org/W2952850066","https://openalex.org/W2169065169","https://openalex.org/W2003295197","https://openalex.org/W3021962464","https://openalex.org/W2130016344","https://openalex.org/W2097396421"],"abstract_inverted_index":{"Abstract":[0],"This":[1,160],"paper":[2],"addresses":[3],"the":[4,8,11,17,30,39,65,104,108,127,188,202,222],"long-standing":[5],"question":[6,106],"of":[7,10,32,38,41,67,111,117,132,149,181,193],"predicativity":[9,105],"Mahlo":[12,20,87,134,175],"universe.":[13,176],"A":[14],"solution,":[15],"called":[16],"extended":[18,85,129,154,173],"predicative":[19,86,130,155,174,211],"universe,":[21],"has":[22,218],"been":[23,219],"proposed":[24],"by":[25,79,201],"Kahle":[26,150],"and":[27,151,210],"Setzer":[28],"in":[29,51,56,75,89,115,136,157,164,198,212,221],"context":[31],"explicit":[33,52,81,158],"mathematics.":[34,159],"It":[35],"makes":[36],"use":[37,180],"collection":[40],"untyped":[42,73],"terms":[43,74,116],"(denoting":[44],"partial":[45],"functions)":[46],"which":[47],"are":[48,208],"directly":[49],"available":[50],"mathematics":[53,82],"but":[54],"not":[55,68],"Martin-L\u00f6f":[57,76,90,112,137,165],"type":[58,77,91,113,138,166,189],"theory.":[59,139],"In":[60,98],"this":[61,99,141],"paper,":[62],"we":[63,101,125,143,178,204],"overcome":[64],"obstacle":[66],"having":[69],"direct":[70],"access":[71],"to":[72,107,119],"theory":[78,92,114,190],"formalizing":[80],"with":[83,93],"an":[84,146,171],"universe":[88,135,156],"certain":[94],"indexed":[95,182,194],"inductive-recursive":[96,183,195],"definitions.":[97],"way,":[100],"can":[102],"relate":[103],"fundamental":[109],"semantics":[110],"computation":[118],"canonical":[120],"form.":[121],"As":[122],"a":[123,133],"result,":[124],"get":[126],"first":[128,144],"definition":[131],"To":[140],"end,":[142],"define":[145],"external":[147],"variant":[148],"Setzer\u2019s":[152],"internal":[153,172],"is":[161],"then":[162],"formalized":[163],"theory,":[167],"where":[168],"it":[169],"becomes":[170],"Although":[177],"make":[179],"definitions":[184,196],"that":[185,206],"go":[186],"beyond":[187],"$\\mathbf":[191],"{IIRD}$":[192],"defined":[197],"previous":[199],"work":[200],"authors,":[203],"argue":[205],"they":[207],"constructive":[209],"Martin-L\u00f6f\u2019s":[213],"sense.":[214],"The":[215],"model":[216],"construction":[217],"type-checked":[220],"proof":[223],"assistant":[224],"Agda.":[225]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-09T08:58:05.943551","created_date":"2025-10-10T00:00:00"}
