{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T17:46:44Z","timestamp":1775497604328,"version":"3.50.1"},"reference-count":17,"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":14346,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1974,12]]},"abstract":"The basic setting of nonstandard analysis consists of a set-theoretical structure together with a map * from into another structure * of the same sort. The function * is taken to be an elementary embedding (in an appropriate sense) and is generally assumed to make * into an enlargement of [13]. The structures and * may be type-hierarchies as in [11] and [13] or they may be cumulative structures with \u03c9<\/jats:italic> levels as in [14]. The assumption that * is an enlargement of has been found to be the weakest hypothesis which allows for the familiar applications of nonstandard analysis in calculus, elementary topology, etc. Indeed, practice has shown that a smooth and useful theory can be achieved only by assuming also that * has some stronger properties such as the saturation properties first introduced in nonstandard analysis by Luxemburg [11].<\/jats:p>This paper concerns an entirely new family of properties, stronger than the saturation properties. For each cardinal number \u03ba<\/jats:italic>, * satisfies the \u03ba-isomorphism property<\/jats:italic> (as an enlargement of ) if the following condition holds:<\/jats:p>For each first order language L with fewer than \u03ba nonlogical symbols, if and are elementarily equivalent structures for L whose domains, relations and functions are all internal (relative to * and ), then and are isomorphic<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2272856","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:32:58Z","timestamp":1146951178000},"page":"717-731","source":"Crossref","is-referenced-by-count":25,"title":["The isomorphism property in nonstandard analysis and its use in the theory of Banach spaces"],"prefix":"10.1017","volume":"39","author":[{"given":"C. Ward","family":"Henson","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200077203_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02788865"},{"key":"S0022481200077203_ref009","first-page":"235","volume-title":"Annals of Mathematics Studies","author":"Lindenstrauss","year":"1972"},{"key":"S0022481200077203_ref016","volume-title":"Mathematical logic","author":"Shoenfield","year":"1967"},{"key":"S0022481200077203_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1966-11606-3"},{"key":"S0022481200077203_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF03008397"},{"key":"S0022481200077203_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1972-0308722-5"},{"key":"S0022481200077203_ref017","first-page":"64","article-title":"Arithmetical classes and types of Boolean algebras (Preliminary report)","volume":"55","author":"Tarski","year":"1949","journal-title":"Bulletin of the American Mathematical Society"},{"key":"S0022481200077203_ref004","article-title":"Subspaces of the nonstandard hull of a normed space","author":"Henson","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200077203_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71555-6"},{"key":"S0022481200077203_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/1970554"},{"key":"S0022481200077203_ref014","first-page":"109","volume-title":"Applications of model theory to algebra, analysis and probability","author":"Robinson","year":"1969"},{"key":"S0022481200077203_ref015","volume-title":"Skrifter utgit av Videnskapsselskapet i Kristiania. I","author":"Skolem","year":"1919"},{"key":"S0022481200077203_ref002","article-title":"The nonstandard hull of a normed Riesz space","author":"Cozart","journal-title":"Duke Mathematics Journal"},{"key":"S0022481200077203_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/sm-49-1-41-50"},{"key":"S0022481200077203_ref013","volume-title":"Non-standard analysis","author":"Robinson","year":"1966"},{"key":"S0022481200077203_ref008","first-page":"1","article-title":"On a theorem of Mackey and Murray","volume":"39","author":"Lindenstrauss","year":"1967","journal-title":"Anais da Academia Brastieira de Ciencias"},{"key":"S0022481200077203_ref011","first-page":"18","volume-title":"Applications of model theory to algebra, analysis and probability","author":"Luxemburg","year":"1969"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200077203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T20:42:54Z","timestamp":1559162574000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200077203\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,12]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1974,12]]}},"alternative-id":["S0022481200077203"],"URL":"https:\/\/doi.org\/10.2307\/2272856","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1974,12]]}}}