{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T09:41:29Z","timestamp":1648546889202},"reference-count":16,"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":5580,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1998,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In \u00a71 we prove that Loeb spaces are compact under various assumptions, and in \u00a72 we prove that Loeb spaces are not compact under various other assumptions. The results in \u00a71 and \u00a72 give a quite complete answer to a question of D.Ross in [9], [11] and [12].<\/jats:p>","DOI":"10.2307\/2586655","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:01:33Z","timestamp":1146938493000},"page":"1371-1392","source":"Crossref","is-referenced-by-count":0,"title":["Compactness of Lobe spaces"],"prefix":"10.1017","volume":"63","author":[{"given":"Renling","family":"Jin","sequence":"first","affiliation":[]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200014304_ref016","volume-title":"Foundation of infinitesimal stochastic analysis","author":"Stroyan","year":"1986"},{"key":"S0022481200014304_ref014","unstructured":"Shelah S. , Cellularity offree products of Boolean algebra, Fundamenta Mathematicae, to appear."},{"key":"S0022481200014304_ref013","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-96-03274-1"},{"key":"S0022481200014304_ref006","volume-title":"Set theory\u2014an introduction to independence proofs","author":"Kunen","year":"1980"},{"key":"S0022481200014304_ref009","unstructured":"Ross D. A. , Measurable transformations in saturated models of analysis, Ph.D. thesis , University of Wisconsin-Madison, 1983."},{"key":"S0022481200014304_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1995-1213854-4"},{"key":"S0022481200014304_ref001","volume-title":"Nonstandard methods in stochastic analysis and mathematical physics","author":"Albeverio","year":"1986"},{"key":"S0022481200014304_ref010","first-page":"1233","volume":"55","author":"Ross","year":"1990","journal-title":"The special model axiom in nonstandard analysis"},{"key":"S0022481200014304_ref004","volume-title":"Handbook of boolean algebra","volume":"3","author":"Fremlin","year":"1989"},{"key":"S0022481200014304_ref012","first-page":"178","volume-title":"Developments in nonstandard mathematics","volume":"336","author":"Ross","year":"1995"},{"key":"S0022481200014304_ref003","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200014304_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF02483083"},{"key":"S0022481200014304_ref005","first-page":"975","volume":"57","author":"Jin","year":"1992","journal-title":"The isomorphism property versus the special model axiom"},{"key":"S0022481200014304_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1992-1079898-8"},{"key":"S0022481200014304_ref007","volume-title":"Handbook of set theoretic topology","author":"Kunen","year":"1984"},{"key":"S0022481200014304_ref008","volume-title":"Nonstandard analysis and its application","author":"Lindstrom","year":"1988"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200014304","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T19:52:08Z","timestamp":1557517928000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200014304\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,12]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,12]]}},"alternative-id":["S0022481200014304"],"URL":"https:\/\/doi.org\/10.2307\/2586655","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,12]]}}}