{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T15:53:29Z","timestamp":1648828409275},"reference-count":14,"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":5945,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1997,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Type two cuts, bad cuts and very bad cuts are introduced in [10] for studying the relationship between Loeb measure and U-topology of a hyperfinite time line in an <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>-saturated nonstandard universe. The questions concerning the existence of those cuts are asked there. In this paper we answer, fully or partially, some of those questions by showing that: (1) type two cuts exist, (2) the \u2135<jats:sub>1<\/jats:sub>-isomorphism property implies that bad cuts exist, but no bad cuts are very bad.<\/jats:p>","DOI":"10.2307\/2275640","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T23:03:06Z","timestamp":1146956586000},"page":"1241-1252","source":"Crossref","is-referenced-by-count":3,"title":["Type two cuts, bad cuts and very bad cut"],"prefix":"10.1017","volume":"62","author":[{"given":"Renling","family":"Jin","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200015723_ref005","first-page":"522","volume":"57","author":"Jin","year":"1992","journal-title":"Cuts in hyperfinite time lines"},{"key":"S0022481200015723_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90078-R"},{"key":"S0022481200015723_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757274"},{"key":"S0022481200015723_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/BF02758648"},{"key":"S0022481200015723_ref001","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200015723_ref002","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-3.3.493"},{"key":"S0022481200015723_ref003","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":"S0022481200015723_ref006","first-page":"975","volume":"57","author":"Jin","year":"1992","journal-title":"The isomorphism property versus the special model axiom"},{"key":"S0022481200015723_ref007","first-page":"1011","volume":"57","author":"Jin","year":"1992","journal-title":"A theoremon the isomorphism property"},{"key":"S0022481200015723_ref009","first-page":"292","volume":"59","author":"Jin","year":"1994","journal-title":"The strength of the isomorphism property"},{"key":"S0022481200015723_ref010","first-page":"71","volume":"56","author":"Keisler","year":"1991","journal-title":"Meager sets on the hyperfinite time line"},{"key":"S0022481200015723_ref011","volume-title":"Nonstandard analysis and its application","author":"Lindstrom","year":"1988"},{"key":"S0022481200015723_ref012","first-page":"512","volume":"60","author":"Schmerl","year":"1995","journal-title":"The isomorphism property for nonstandard universes"},{"key":"S0022481200015723_ref014","volume-title":"Foundation of infinitesimal stochastic analysis","author":"Stroyan","year":"1986"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200015723","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T19:54:40Z","timestamp":1557604480000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200015723\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1997,12]]}},"alternative-id":["S0022481200015723"],"URL":"https:\/\/doi.org\/10.2307\/2275640","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,12]]}}}