{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T17:58:46Z","timestamp":1698602326907},"reference-count":9,"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":8593,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:p><jats:italic>\u03ba<\/jats:italic>-saturation [SL] is probably the single most useful property of nonstandard models of analysis. For some applications, however, stronger saturation hypotheses seem necessary. Henson formulated his elegant <jats:italic>\u03ba-isomorphism property<\/jats:italic> (see [H1], and \u00a72 below) to address this need. This property, though well-suited to certain situations (notably those arising in Banach space theory), is often difficult to apply in practice (see [SL, \u00a77.7]).<\/jats:p><jats:p>In this paper I describe an alternative to <jats:italic>\u03ba<\/jats:italic>-isomorphism which is much easier to use; in particular, a proof which assumes that the nonstandard model is <jats:italic>fully<\/jats:italic> saturated can usually be converted directly to one using this <jats:italic>special model<\/jats:italic> axiom.<\/jats:p><jats:p>Precise definitions of both these axioms appear in \u00a72. In \u00a73 I prove some simple properties of the special model axiom, one of which is that it is at least as strong as <jats:italic>\u03ba<\/jats:italic>-isomorphism. In \u00a7\u00a74, 5, and 6 the axiom is used to construct a few examples, many of which are pathological, or at the very least counterintuitive. (These examples are given primarily to illustrate use of the axiom; the only one of independent interest is Theorem 5.5.) In \u00a77 some alternative axioms and open problems are discussed.<\/jats:p><jats:p>Many of the results in this paper grew out of discussion and correspondence with C. Ward Henson, to whom I am consequently most grateful.<\/jats:p>","DOI":"10.2307\/2274484","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:36:50Z","timestamp":1146955010000},"page":"1233-1242","source":"Crossref","is-referenced-by-count":8,"title":["The special model axiom in nonstandard analysis"],"prefix":"10.1017","volume":"55","author":[{"given":"David","family":"Ross","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025664_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1979-0521888-9"},{"key":"S0022481200025664_ref004","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":"S0022481200025664_ref003","first-page":"317","volume":"52","author":"Forti","year":"1987","journal-title":"On the order structure of the nonstandard real axis"},{"key":"S0022481200025664_ref002","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200025664_ref008","volume-title":"Foundations of infinitesimal analysis","author":"Stroyan","year":"1986"},{"key":"S0022481200025664_ref009","volume-title":"Introduction to the theory of infinitesimals","author":"Stroyan","year":"1976"},{"key":"S0022481200025664_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9339-9"},{"key":"S0022481200025664_ref001","unstructured":"Benninghofen B. , untitled unpublished manuscript."},{"key":"S0022481200025664_ref007","doi-asserted-by":"publisher","DOI":"10.4064\/fm-128-1-29-36"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025664","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T20:24:55Z","timestamp":1558211095000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025664\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1990,9]]}},"alternative-id":["S0022481200025664"],"URL":"https:\/\/doi.org\/10.2307\/2274484","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}