{"id":"https://openalex.org/W4241186888","doi":"https://doi.org/10.2307/2275676","title":"Stretchings","display_name":"Stretchings","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W4241186888","doi":"https://doi.org/10.2307/2275676"},"language":"en","primary_location":{"id":"doi:10.2307/2275676","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275676","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057731005","display_name":"Olivier Finkel","orcid":"https://orcid.org/0000-0002-6461-2941"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"O. Finkel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077096528","display_name":"J.-P. Ressayre","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"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":["FR"],"is_corresponding":false,"raw_author_name":"J. P. Ressayre","raw_affiliation_strings":["Equipe de Logique Math\u00e9matique (URA 753, CNRS), Universit\u00e9 Paris7, 2, Place Jussieu - Case 7012, 75251 Paris Cedex 05, France, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equipe de Logique Math\u00e9matique (URA 753, CNRS), Universit\u00e9 Paris7, 2, Place Jussieu - Case 7012, 75251 Paris Cedex 05, France, E-mail:","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.38919617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"61","issue":"2","first_page":"563","last_page":"585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9670000076293945,"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":0.9441999793052673,"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/axiom","display_name":"Axiom","score":0.6727733612060547},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.665252149105072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6202654242515564},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.6095618009567261},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4918239116668701},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4817947745323181},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4527748227119446},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43146955966949463},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4239111840724945},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.41764092445373535},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1717507541179657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09535181522369385},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09503543376922607},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06104809045791626}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6727733612060547},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.665252149105072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6202654242515564},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.6095618009567261},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4918239116668701},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4817947745323181},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4527748227119446},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43146955966949463},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4239111840724945},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.41764092445373535},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1717507541179657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09535181522369385},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09503543376922607},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06104809045791626},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2275676","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275676","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1574937548","https://openalex.org/W2480761287","https://openalex.org/W4247248535","https://openalex.org/W4248475207","https://openalex.org/W4249826307","https://openalex.org/W6720637135"],"related_works":["https://openalex.org/W2331020993","https://openalex.org/W2972379433","https://openalex.org/W4383764068","https://openalex.org/W1481826604","https://openalex.org/W1797057780","https://openalex.org/W2404739533","https://openalex.org/W255137432","https://openalex.org/W1850316734","https://openalex.org/W4311299684","https://openalex.org/W4360831352"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"structure":[2],"is":[3,11,131],"locally":[4,23],"finite":[5,38,103],"if":[6],"every":[7],"finitely":[8],"generated":[9],"substructure":[10],"finite;":[12],"local":[13,29,44,124,154,164],"sentences":[14,17,30],"are":[15,22],"universal":[16],"all":[18,171],"models":[19,42],"of":[20,43,67,90,99,102,118,122,134,143,162],"which":[21],"finite.":[24],"The":[25],"stretching":[26,85],"theorem":[27,86],"for":[28],"expresses":[31],"a":[32,65,108,123,141,157,163],"remarkable":[33],"reflection":[34],"phenomenon":[35],"between":[36],"the":[37,40,60,84,88,96,112,119,132,175],"and":[39,75,93],"infinite":[41,172],"sentences.":[45],"This":[46],"result":[47],"in":[48,64,79],"part":[49],"requires":[50],"strong":[51],"axioms":[52],"to":[53,111],"be":[54],"proved;":[55],"it":[56],"was":[57],"studied":[58],"by":[59],"second":[61],"named":[62,114],"author,":[63],"paper":[66],"this":[68,77],"Journal,":[69],"volume":[70],"53.":[71],"Here":[72],"we":[73,81,106],"correct":[74],"extend":[76],"paper;":[78],"particular":[80],"show":[82],"that":[83,138,149,168],"implies":[87],"existence":[89,161],"inaccessible":[91,176],"cardinals,":[92],"has":[94,140],"precisely":[95],"consistency":[97],"strength":[98],"Mahlo":[100],"cardinals":[101],"order.":[104],"And":[105],"present":[107],"sequel":[109],"due":[110],"first":[113],"author:":[115],"(i)":[116],"decidability":[117],"spectrum":[120],"Sp(\u03c6)":[121,130,169],"sentence":[125,155,165],"\u03c6,":[126],"below":[127],"\u03c9\u03c9;":[128],"where":[129],"set":[133],"ordinals":[135,173],"\u03b1":[136,146],"such":[137,167],"\u03c6":[139,153,166],"model":[142],"order":[144],"type":[145],"(ii)":[147],"proof":[148],"beth\u03c9":[150],"=":[151],"sup{Sp(\u03c6):":[152],"with":[156],"bounded":[158],"spectrum}":[159],"(iii)":[160],"contains":[170],"except":[174],"cardinals.":[177]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2022-05-12T00:00:00"}