{"id":"https://openalex.org/W2024325951","doi":"https://doi.org/10.1002/malq.200610049","title":"Local sentences and Mahlo cardinals","display_name":"Local sentences and Mahlo cardinals","publication_year":2007,"publication_date":"2007-09-26","ids":{"openalex":"https://openalex.org/W2024325951","doi":"https://doi.org/10.1002/malq.200610049","mag":"2024325951"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200610049","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200610049","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0705.2298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057731005","display_name":"Olivier Finkel","orcid":"https://orcid.org/0000-0002-6461-2941"},"institutions":[{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Olivier Finkel","raw_affiliation_strings":["Laboratoire de l'Informatique du Parall\u00e9lisme"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de l'Informatique du Parall\u00e9lisme","institution_ids":["https://openalex.org/I4210144566"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018265011","display_name":"Stevo Todor\u010devi\u0107","orcid":"https://orcid.org/0000-0003-4543-7962"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]}],"countries":["CA","FR"],"is_corresponding":true,"raw_author_name":"Stevo Todorcevic","raw_affiliation_strings":["Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4","U.F.R. de Mathe\u0301matiques, Universite\u0301 Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France","U.F.R.\u00a0de Math\u00e9matiques, Universit\u00e9 Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"U.F.R. de Mathe\u0301matiques, Universite\u0301 Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884"]},{"raw_affiliation_string":"U.F.R.\u00a0de Math\u00e9matiques, Universit\u00e9 Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018265011","https://openalex.org/A5057731005"],"corresponding_institution_ids":["https://openalex.org/I185261750","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I4210144566"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10886238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"53","issue":"6","first_page":"558","last_page":"563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.991599977016449,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9850000143051147,"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/mathematics","display_name":"Mathematics","score":0.6806589365005493},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6601762175559998},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6434546709060669},{"id":"https://openalex.org/keywords/regular-cardinal","display_name":"Regular cardinal","score":0.6213499903678894},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.5433375239372253},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5171584486961365},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5041450262069702},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.48043036460876465},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4638075828552246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4627634882926941},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4418381154537201},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3292807340621948},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1532500684261322},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07024261355400085},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.048940509557724}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6806589365005493},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6601762175559998},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6434546709060669},{"id":"https://openalex.org/C89507440","wikidata":"https://www.wikidata.org/wiki/Q1193137","display_name":"Regular cardinal","level":2,"score":0.6213499903678894},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.5433375239372253},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5171584486961365},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5041450262069702},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48043036460876465},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4638075828552246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4627634882926941},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4418381154537201},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3292807340621948},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1532500684261322},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07024261355400085},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.048940509557724},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.200610049","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200610049","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0705.2298","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0705.2298","pdf_url":"https://arxiv.org/pdf/0705.2298","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0705.2298","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0705.2298","pdf_url":"https://arxiv.org/pdf/0705.2298","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2008877412","https://openalex.org/W2035637454","https://openalex.org/W2057797149","https://openalex.org/W2083828428","https://openalex.org/W2140765313","https://openalex.org/W2569306015","https://openalex.org/W4241186888","https://openalex.org/W4243898315","https://openalex.org/W4249826307"],"related_works":["https://openalex.org/W178365807","https://openalex.org/W4240676090","https://openalex.org/W2081441417","https://openalex.org/W2375873920","https://openalex.org/W1970375080","https://openalex.org/W4386544785","https://openalex.org/W16157476","https://openalex.org/W1555836633","https://openalex.org/W4300886224","https://openalex.org/W2103798851"],"abstract_inverted_index":{"Abstract":[0],"Local":[1],"sentences":[2,26],"were":[3,41],"introduced":[4],"by":[5,101],"Ressayre":[6],"in":[7,60],"[6]":[8],"who":[9],"proved":[10,43],"certain":[11,45],"remarkable":[12],"stretching":[13,39,82],"theorems":[14,40],"establishing":[15],"the":[16,19,28,50,81,87],"equivalence":[17],"between":[18],"existence":[20,29,88],"of":[21,30,37,52,71,89,121],"finite":[22],"models":[23,120],"for":[24,93,105,126],"these":[25,38],"and":[27],"some":[31],"infinite":[32,128],"well":[33,118],"ordered":[34,119],"models.":[35],"Two":[36],"only":[42],"under":[44],"large":[46],"cardinal":[47],"axioms":[48],"but":[49],"question":[51],"their":[53],"exact":[54],"(consistency)":[55],"strength":[56],"was":[57],"left":[58],"open":[59],"[4].":[61],"Here":[62],"we":[63,78],"solve":[64],"this":[65],"problem,":[66],"using":[67],"a":[68,112],"combinatorial":[69],"result":[70],"J.":[72],"H.":[73],"Schmerl":[74],"[7].":[75],"In":[76],"fact,":[77],"show":[79],"that":[80,104],"principles":[83],"are":[84],"equivalent":[85],"to":[86],"n":[90,96,108,116,137],"\u2010Mahlo":[91,138],"cardinals":[92],"appropriate":[94],"integers":[95],".":[97],"This":[98],"is":[99,111,134],"done":[100],"proving":[102],"first":[103],"every":[106,127],"integer":[107],",":[109,125],"there":[110],"local":[113],"sentence":[114],"\u03c6":[115],"having":[117],"order":[122],"type":[123],"\u03c4":[124,130],"ordinal":[129],">":[131],"\u03c9":[132],"which":[133],"not":[135],"an":[136],"cardinal.":[139],"(\u00a9":[140],"2007":[141],"WILEY\u2010VCH":[142],"Verlag":[143],"GmbH":[144],"&":[145],"Co.":[146],"KGaA,":[147],"Weinheim)":[148]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}