{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T16:26:55Z","timestamp":1767198415088,"version":"build-2238731810"},"reference-count":17,"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":8228,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1991,9]]},"abstract":"Abstract<\/jats:title>\n \n In a nonstandard universe, the\n \u03ba<\/jats:italic>\n -saturation property states that any family of fewer than\n \u03ba<\/jats:italic>\n internal sets with the finite intersection property has a nonempty intersection. An ordered field\n F<\/jats:italic>\n is said to have the\n \u03bb<\/jats:italic>\n -Bolzano-Weierstrass property iff\n F<\/jats:italic>\n has cofinality\n \u03bb<\/jats:italic>\n and every bounded\n \u03bb<\/jats:italic>\n -sequence in\n F<\/jats:italic>\n has a convergent\n \u03bb<\/jats:italic>\n -subsequence. We show that if\n \u03ba<\/jats:italic>\n <\n \u03bb<\/jats:italic>\n are uncountable regular cardinals and\n \n \u03b2\n \u03b1<\/jats:sup>\n <\/jats:italic>\n <\n \u03bb<\/jats:italic>\n whenever\n \u03b1<\/jats:italic>\n <\n \u03ba<\/jats:italic>\n and\n \u03b2<\/jats:italic>\n <\n \u03bb<\/jats:italic>\n then there is a\n \u03ba<\/jats:italic>\n -saturated nonstandard universe in which the hyperreal numbers have the\n \u03bb<\/jats:italic>\n -Bolzano-Weierstrass property. The result also applies to certain fragments of set theory and second order arithmetic.\n <\/jats:p>","DOI":"10.2307\/2275069","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:41:03Z","timestamp":1146940863000},"page":"1016-1025","source":"Crossref","is-referenced-by-count":9,"title":["Making the hyperreal line both saturated and complete"],"prefix":"10.1017","volume":"56","author":[{"given":"H. Jerome","family":"Keisler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James H.","family":"Schmerl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200024178_ref017","first-page":"195","volume-title":"Applications of model theory to algebra, analysis, and probability","author":"Zakon","year":"1969"},{"key":"S0022481200024178_ref016","first-page":"69","article-title":"On an ordered algebraic field","volume":"41","author":"Sikorski","year":"1948","journal-title":"Comptes Rendus des S\u00e9ances de la Soci\u00e9t\u00e9 des Sciences et des Lettres de Varsovie, Classe III"},{"key":"S0022481200024178_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90013-1"},{"key":"S0022481200024178_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90009-8"},{"key":"S0022481200024178_ref013","first-page":"274","volume-title":"Applications of model theory to algebra, analysis, and probability","author":"Scott","year":"1969"},{"key":"S0022481200024178_ref012","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0846594-0"},{"key":"S0022481200024178_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761121"},{"key":"S0022481200024178_ref009","first-page":"257","volume-title":"Infinitistic methods (proceedings, Warsaw 1959)","author":"MacDowell","year":"1961"},{"key":"S0022481200024178_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066005"},{"key":"S0022481200024178_ref003","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870226"},{"key":"S0022481200024178_ref002","volume-title":"Model theory","author":"Chang","year":"1990"},{"key":"S0022481200024178_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0090952"},{"key":"S0022481200024178_ref004","first-page":"365","volume":"46","author":"Kamo","year":"1981","journal-title":"Nonstandard natural number systems and nonstandard models"},{"key":"S0022481200024178_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0080973"},{"key":"S0022481200024178_ref005","doi-asserted-by":"publisher","DOI":"10.21099\/tkbjm\/1496159315"},{"key":"S0022481200024178_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1977-0476498-7"},{"key":"S0022481200024178_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/025\/0357108"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200024178","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T06:35:03Z","timestamp":1679466903000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200024178\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,9]]},"references-count":17,"aliases":["10.2178\/jsl\/1183743748"],"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,9]]}},"alternative-id":["S0022481200024178"],"URL":"https:\/\/doi.org\/10.2307\/2275069","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,9]]}}}