{"id":"https://openalex.org/W7130590437","doi":"https://doi.org/10.1016/j.apal.2026.103740","title":"Induction on dilators and Bachmann-Howard fixed points","display_name":"Induction on dilators and Bachmann-Howard fixed points","publication_year":2026,"publication_date":"2026-02-19","ids":{"openalex":"https://openalex.org/W7130590437","doi":"https://doi.org/10.1016/j.apal.2026.103740"},"language":"en","primary_location":{"id":"doi:10.1016/j.apal.2026.103740","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.apal.2026.103740","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.apal.2026.103740","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126441283","display_name":"Juan P. Aguilera","orcid":null},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Juan P. Aguilera","raw_affiliation_strings":["Institut f\u00fcr diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071872554","display_name":"Anton Freund","orcid":"https://orcid.org/0000-0002-5456-5790"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Anton Freund","raw_affiliation_strings":["University of W\u00fcrzburg, Institute of Mathematics, Emil-Fischer-Str. 40, 97074 W\u00fcrzburg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5456-5790","affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg, Institute of Mathematics, Emil-Fischer-Str. 40, 97074 W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056618682","display_name":"Andreas Weiermann","orcid":"https://orcid.org/0000-0002-5561-5323"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Andreas Weiermann","raw_affiliation_strings":["Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281 S8, 9000 Ghent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281 S8, 9000 Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056618682","https://openalex.org/A5071872554","https://openalex.org/A5126441283"],"corresponding_institution_ids":["https://openalex.org/I145847075","https://openalex.org/I25974101","https://openalex.org/I32597200"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":{"value":3390,"currency":"USD","value_usd":3390},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31695765,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"177","issue":"7","first_page":"103740","last_page":"103740"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.6116999983787537,"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":0.6116999983787537,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.0471000000834465,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.032600000500679016,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/functor","display_name":"Functor","score":0.748199999332428},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7389000058174133},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6444000005722046},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.48019999265670776},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.45399999618530273},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4171000123023987},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.41600000858306885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7849000096321106},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.748199999332428},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7389000058174133},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6444000005722046},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.48019999265670776},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.41600000858306885},{"id":"https://openalex.org/C206743973","wikidata":"https://www.wikidata.org/wiki/Q178377","display_name":"Mathematical induction","level":2,"score":0.4047999978065491},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37540000677108765},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.36820000410079956},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3675999939441681},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C153778094","wikidata":"https://www.wikidata.org/wiki/Q357858","display_name":"Adjoint functors","level":3,"score":0.2921000123023987},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2696000039577484}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.apal.2026.103740","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.apal.2026.103740","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.apal.2026.103740","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.apal.2026.103740","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1608253100","display_name":null,"funder_award_id":"STA-139","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3852438965","display_name":null,"funder_award_id":"460597863","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1443608663","https://openalex.org/W1980969069","https://openalex.org/W2025460262","https://openalex.org/W2027194639","https://openalex.org/W2052953762","https://openalex.org/W2088408332","https://openalex.org/W2317130416","https://openalex.org/W2890902398","https://openalex.org/W2891240794","https://openalex.org/W2940438007","https://openalex.org/W2952241302","https://openalex.org/W3022466210","https://openalex.org/W3094559094","https://openalex.org/W3132012723","https://openalex.org/W4234245490","https://openalex.org/W4255491203","https://openalex.org/W4387576584","https://openalex.org/W4409361127","https://openalex.org/W4412747380"],"related_works":[],"abstract_inverted_index":{"One":[0],"of":[1,6,34,43,57,129,145],"the":[2,32,39,65,103,107,127],"most":[3],"important":[4],"principles":[5],"J.-Y.":[7],"Girard's":[8],"\u03a0":[9,44,90,120],"2":[10],"1":[11,45,46,91,92,121,122],"-logic":[12],"is":[13,36,124],"induction":[14,111],"on":[15,112],"dilators.":[16,113],"In":[17],"particular,":[18],"Girard":[19,52],"used":[20],"this":[21,75],"principle":[22,109],"to":[23,38,74,86,110,117,126,134],"construct":[24],"his":[25],"famous":[26],"functor":[27,131],"\u039b.":[28,146],"He":[29],"claimed":[30],"that":[31,64,119],"totality":[33,128],"\u039b":[35],"equivalent":[37,125],"set":[40],"existence":[41],"axiom":[42],"-comprehension":[47,93,123],"from":[48],"reverse":[49],"mathematics.":[50],"While":[51],"provided":[53],"a":[54,58,81,95,130,142],"plausible":[55],"description":[56],"proof":[59],"around":[60],"1980,":[61],"it":[62],"seems":[63],"very":[66],"technical":[67],"details":[68],"have":[69],"not":[70],"been":[71],"worked":[72],"out":[73],"day.":[76],"A":[77],"few":[78],"years":[79],"ago,":[80],"loosely":[82],"related":[83],"approach":[84],"led":[85],"an":[87],"equivalence":[88],"between":[89],"and":[94],"certain":[96],"Bachmann-Howard":[97,108],"principle.":[98],"The":[99],"present":[100],"paper":[101],"closes":[102],"circle.":[104],"We":[105],"relate":[106],"This":[114],"allows":[115],"us":[116],"show":[118],"J":[132],"due":[133],"P.":[135],"P\u00e4ppinghaus,":[136],"which":[137],"can":[138],"be":[139],"seen":[140],"as":[141],"streamlined":[143],"version":[144]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-02-20T00:00:00"}
