{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T13:39:38Z","timestamp":1649079578620},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":7862,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1992,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline1\" \/>-structure is called internally presented in a nonstandard universe if its base set and interpretation of every symbol in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline1\" \/> are internal. A nonstandard universe is said to satisfy the <jats:italic>\u03ba<\/jats:italic>-isomorphism property if for any two internally presented <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline1\" \/>-structures <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline2\" \/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline3\" \/>, where <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline1\" \/> has less than <jats:italic>\u03ba<\/jats:italic> many symbols, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline2\" \/> is elementarily equivalent to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline3\" \/> implies that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline2\" \/> is isomorphic to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200022507_inline3\" \/>. In this paper we prove that the \u2135<jats:sub>1<\/jats:sub>-isomorphism property is equivalent to the \u2135<jats:sub>0<\/jats:sub>-isomorphism property plus \u2135<jats:sub>1<\/jats:sub>-saturation.<\/jats:p>","DOI":"10.2307\/2275446","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:45:35Z","timestamp":1146955535000},"page":"1011-1017","source":"Crossref","is-referenced-by-count":5,"title":["A theorem on the isomorphism property"],"prefix":"10.1017","volume":"57","author":[{"given":"Renling","family":"Jin","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200022507_ref005","unstructured":"Henson C. Ward , Private communication."},{"key":"S0022481200022507_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02756565"},{"key":"S0022481200022507_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757274"},{"key":"S0022481200022507_ref001","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200022507_ref002","first-page":"717","volume":"39","author":"Henson","year":"1974","journal-title":"The isomorphism property in nonstandard analysis and its use in the theory of Banach space"},{"key":"S0022481200022507_ref006","volume":"57","author":"Jin","year":"1992","journal-title":"The isomorphism property versus the special model axiom"},{"key":"S0022481200022507_ref007","first-page":"1233","volume":"55","author":"Ross","year":"1990","journal-title":"\u201cThe special model axiom in nonstandard analysis"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200022507","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T21:00:53Z","timestamp":1558040453000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200022507\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,9]]}},"alternative-id":["S0022481200022507"],"URL":"https:\/\/doi.org\/10.2307\/2275446","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,9]]}}}