{"id":"https://openalex.org/W2107539861","doi":"https://doi.org/10.1142/s0219061312500018","title":"THE STABILITY SPECTRUM FOR CLASSES OF ATOMIC MODELS","display_name":"THE STABILITY SPECTRUM FOR CLASSES OF ATOMIC MODELS","publication_year":2012,"publication_date":"2012-04-20","ids":{"openalex":"https://openalex.org/W2107539861","doi":"https://doi.org/10.1142/s0219061312500018","mag":"2107539861"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061312500018","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061312500018","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/The_Stability_spectrum_for_classes_of_atomic_models/10772156","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037915949","display_name":"John T. Baldwin","orcid":"https://orcid.org/0000-0002-0185-5196"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JOHN T. BALDWIN","raw_affiliation_strings":["Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan St. (M/C 249), Chicago, IL 60607-7045, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan St. (M/C 249), Chicago, IL 60607-7045, USA","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024923217","display_name":"Saharon Shelah","orcid":"https://orcid.org/0000-0003-0462-3152"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"SAHARON SHELAH","raw_affiliation_strings":["Department of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904 Girat Ram, Israel","Rutgers University, New Brunswick, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904 Girat Ram, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"Rutgers University, New Brunswick, NJ, USA","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6771,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.83257175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"01","first_page":"1250001","last_page":"1250001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9977999925613403,"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":0.9977999925613403,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9628000259399414,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9555000066757202,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8525215983390808},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.7060465812683105},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6065086722373962},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5906422138214111},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5843330025672913},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5129344463348389},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5102221965789795},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4593278765678406},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43542250990867615},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4333834946155548},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2846824526786804},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06274420022964478},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05814489722251892},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05640619993209839}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8525215983390808},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.7060465812683105},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6065086722373962},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5906422138214111},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5843330025672913},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5129344463348389},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5102221965789795},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4593278765678406},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43542250990867615},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4333834946155548},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2846824526786804},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06274420022964478},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05814489722251892},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05640619993209839},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":5,"locations":[{"id":"doi:10.1142/s0219061312500018","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061312500018","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.6700","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.6700","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uic.edu/~jbaldwin/pub/spec15.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.216.999","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.216.999","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uic.edu/%7Ejbaldwin/pub/spec15.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.573.3357","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.573.3357","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.math.uic.edu/~jbaldwin/pub/spec14.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/10772156","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/The_Stability_spectrum_for_classes_of_atomic_models/10772156","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/10772156","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/The_Stability_spectrum_for_classes_of_atomic_models/10772156","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W65053296","https://openalex.org/W84496008","https://openalex.org/W1026721552","https://openalex.org/W1499179478","https://openalex.org/W1523486281","https://openalex.org/W1537266584","https://openalex.org/W1596591404","https://openalex.org/W1965265111","https://openalex.org/W1997290756","https://openalex.org/W2005659848","https://openalex.org/W2010730711","https://openalex.org/W2032547196","https://openalex.org/W2047282968","https://openalex.org/W2047460779","https://openalex.org/W2049252038","https://openalex.org/W2063628115","https://openalex.org/W2066047363","https://openalex.org/W2077904586","https://openalex.org/W2081441842","https://openalex.org/W2087176240","https://openalex.org/W2134675812","https://openalex.org/W2594827049","https://openalex.org/W2799061192","https://openalex.org/W4213347674","https://openalex.org/W4231373458","https://openalex.org/W4253242082"],"related_works":["https://openalex.org/W2121543990","https://openalex.org/W1981078319","https://openalex.org/W2402800040","https://openalex.org/W2000020320","https://openalex.org/W4252969132","https://openalex.org/W2008917324","https://openalex.org/W2581541046","https://openalex.org/W4387315838","https://openalex.org/W2788478146","https://openalex.org/W4298062283"],"abstract_inverted_index":{"We":[0],"prove":[1],"two":[2],"results":[3,126],"on":[4,142,192],"the":[5,135,143,155,160,169,193],"stability":[6],"spectrum":[7,144],"for":[8,34,39,45,61,76,82,110,134,174,187],"L":[9,177],"\u03c9":[10,178],"1":[11,179],",\u03c9":[12,180],".":[13,181],"Here":[14],"[Formula:":[15,57,71,106],"see":[16,58,72,107],"text]":[17],"denotes":[18],"an":[19,52,68],"appropriate":[20],"notion":[21],"(at":[22],"or":[23],"mod)":[24],"of":[25,28,131,145,157,171,176,190],"Stone":[26],"space":[27],"m-types":[29],"over":[30],"M.":[31],"(1)":[32],"Theorem":[33,75],"unstable":[35,136],"case:":[36,79],"Suppose":[37,80],"that":[38,81,95],"some":[40,140,185],"positive":[41],"integer":[42],"m":[43],"and":[44,105,138],"every":[46,62,83],"\u03b1":[47,84,91,97,100,104],"<":[48,85],"\u03b4(T),":[49],"there":[50,66,88],"is":[51,67,89,120],"M":[53,69,90],"\u2208":[54,92],"K":[55,93,119],"with":[56,70,113],"text].":[59,73,108],"Then":[60,109],"\u03bb":[63,96],"\u2265":[64,102],"|T|,":[65],"(2)":[74],"strictly":[77,146],"stable":[78,147],"\u03b4":[86],"(T),":[87],"such":[94],"=":[98],"|M":[99],"|":[101],"\u2136":[103],"any":[111],"\u03bc":[112,114],"\u2135":[115],"0":[116],">":[117],"\u03bc,":[118],"not":[121],"i-stable":[122],"in":[123,149,159],"\u03bc.":[124],"These":[125],"provide":[127,184],"a":[128,188],"new":[129],"kind":[130],"sufficient":[132],"condition":[133],"case":[137],"shed":[139],"light":[141],"theories":[148],"this":[150,165],"context.":[151],"The":[152],"methods":[153],"avoid":[154],"use":[156],"compactness":[158],"theory":[161],"under":[162],"study.":[163],"In":[164],"paper,":[166],"we":[167,183],"expound":[168],"construction":[170],"tree":[172],"indiscernibles":[173],"sentences":[175],"Further":[182],"context":[186],"number":[189],"variants":[191],"Ehrenfeucht\u2013Mostowski":[194],"construction.":[195]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}