{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T14:26:14Z","timestamp":1766759174890},"reference-count":9,"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":6310,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>If <jats:italic>T<\/jats:italic> has only countably many complete types, yet has a type of infinite multiplicity then there is a c.c.c. forcing notion <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200016911_inline1\" \/> such that, in any <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200016911_inline1\" \/>-generic extension of the universe, there are non-isomorphic models <jats:italic>M<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>M<\/jats:italic><jats:sub>2<\/jats:sub> of <jats:italic>T<\/jats:italic> that can be forced isomorphic by a c.c.c. forcing. We give examples showing that the hypothesis on the number of complete types is necessary and what happens if \u2018c.c.c\u2019 is replaced by other cardinal-preserving adjectives. We also give an example showing that membership in a pseudo-elementary class can be altered by very simple cardinal-preserving forcings.<\/jats:p>","DOI":"10.2307\/2275818","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:59:54Z","timestamp":1146956394000},"page":"1305-1320","source":"Crossref","is-referenced-by-count":2,"title":["Forcing isomorphism II"],"prefix":"10.1017","volume":"61","author":[{"given":"M. C.","family":"Laskowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Shelah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200016911_ref009","volume-title":"Classification theory","author":"Shelah","year":"1991"},{"key":"S0022481200016911_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760649"},{"key":"S0022481200016911_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07330-8"},{"key":"S0022481200016911_ref002","volume":"58","author":"Baldwin","year":"1993","journal-title":"Forcing isomorphism"},{"key":"S0022481200016911_ref003","first-page":"5","volume-title":"Studies in model theory","author":"Barwise","year":"1973"},{"key":"S0022481200016911_ref004","volume-title":"Set theory","author":"Kunen","year":"1980"},{"key":"S0022481200016911_ref005","volume-title":"Stability in model theory","author":"Lascar","year":"1987"},{"key":"S0022481200016911_ref007","volume-title":"The Haar integral","author":"Nachbin","year":"1965"},{"key":"S0022481200016911_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90005-4"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200016911","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T19:59:52Z","timestamp":1557691192000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200016911\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,12]]}},"alternative-id":["S0022481200016911"],"URL":"https:\/\/doi.org\/10.2307\/2275818","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12]]}}}