{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T11:10:11Z","timestamp":1708427411937},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4119,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider a small supersimple theory with a property (CS) (close to stability). We prove that if in such a theory<jats:italic>T<\/jats:italic>there is a type<jats:italic>p<\/jats:italic>\u2208<jats:italic>S<\/jats:italic>(<jats:italic>A<\/jats:italic>) (where<jats:italic>A<\/jats:italic>is finite) with<jats:italic>SU<\/jats:italic>(<jats:italic>p<\/jats:italic>) = 1 and infinitely many extensions over<jats:italic>acl<jats:sup>eq<\/jats:sup><\/jats:italic>(<jats:italic>A<\/jats:italic>), then in<jats:italic>T<\/jats:italic>there is a modular such type. Also, if<jats:italic>T<\/jats:italic>is supersimple with (CS) and<jats:italic>p<\/jats:italic>\u2208<jats:italic>S<\/jats:italic>(\u2205) is isolated,<jats:italic>SU<\/jats:italic>(<jats:italic>p<\/jats:italic>) = 1 and<jats:italic>p<\/jats:italic>has infinitely many extensions over<jats:italic>acl<jats:sup>eq<\/jats:sup><\/jats:italic>(\u2205), then<jats:italic>p<\/jats:italic>is modular.<\/jats:p>","DOI":"10.2178\/jsl\/1190150302","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:16:54Z","timestamp":1197573414000},"page":"1601-1615","source":"Crossref","is-referenced-by-count":0,"title":["Modular types in some supersimple theories"],"prefix":"10.1017","volume":"67","author":[{"given":"Ludomir","family":"Newelski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009245_ref014","first-page":"98","article-title":"Strongly minimal countably categorical theories","volume":"21","author":"Zilber","year":"1980","journal-title":"Sibirskii Mathematicheskii Zhurnal"},{"key":"S0022481200009245_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3002-0"},{"key":"S0022481200009245_ref012","first-page":"177","article-title":"Simple unstable theories","volume":"19","author":"Shelah","year":"1980","journal-title":"Annals of Pure and Applied Logic"},{"key":"S0022481200009245_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-01-02854-9"},{"key":"S0022481200009245_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)90028-0"},{"key":"S0022481200009245_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-00-00350-7"},{"key":"S0022481200009245_ref001","first-page":"1044","volume":"50","author":"Buechler","year":"1985","journal-title":"The geometry of weakly minimal types"},{"key":"S0022481200009245_ref004","unstructured":"de Piro T. and Kim B. , The geometry of 1-based minimal type, manuscript, 2001."},{"key":"S0022481200009245_ref009","doi-asserted-by":"publisher","DOI":"10.4064\/fm-146-2-121-139"},{"key":"S0022481200009245_ref011","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534372.001.0001","volume-title":"Geometric Stability Theory","author":"Pillay","year":"1996"},{"key":"S0022481200009245_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(85)90023-5"},{"key":"S0022481200009245_ref005","first-page":"293","volume":"65","author":"Hart","year":"2000","journal-title":"Coordinatization and canonical bases in simple theories"},{"key":"S0022481200009245_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082236"},{"key":"S0022481200009245_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(97)00019-5"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T10:42:47Z","timestamp":1708425767000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009245\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2002,12]]}},"alternative-id":["S0022481200009245"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150302","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}