{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T23:21:31Z","timestamp":1692832891721},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6585,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Using Steel's recent result that assuming AD, in <jats:italic>L<\/jats:italic>[\u211d] below \u0398, <jats:italic>\u03ba<\/jats:italic> is regular iff <jats:italic>\u03ba<\/jats:italic> is measurable, we mimic below \u0398 certain earlier results of Gitik. In particular, we construct via forcing a model in which all uncountable cardinals below \u0398 are singular and a model in which the only regular uncountable cardinal below \u0398 is \u2135<jats:sub>1<\/jats:sub>.<\/jats:p>","DOI":"10.2307\/2275606","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:57:36Z","timestamp":1146941856000},"page":"225-235","source":"Crossref","is-referenced-by-count":8,"title":["AD and patterns of singular cardinals below \u0398"],"prefix":"10.1017","volume":"61","author":[{"given":"Arthur W.","family":"Apter","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017722_ref020","unstructured":"Steel J. , paper 1, in preparation."},{"key":"S0022481200017722_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90009-X"},{"key":"S0022481200017722_ref017","volume-title":"Descriptive set theory","author":"Moschovakis","year":"1980"},{"key":"S0022481200017722_ref015","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.85.18.6582"},{"key":"S0022481200017722_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771612"},{"key":"S0022481200017722_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/S0003-4843(77)80002-8"},{"key":"S0022481200017722_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0090236"},{"key":"S0022481200017722_ref009","first-page":"271","volume-title":"Proceedings of symposia in pure mathematics","author":"Kechris","year":"1985"},{"key":"S0022481200017722_ref003","unstructured":"Cummings J. and Woodin H. , Generalised Prikry forcings, circulated manuscript of a forthcoming book."},{"key":"S0022481200017722_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01269948"},{"key":"S0022481200017722_ref021","unstructured":"Steel J. , paper 2, in preparation."},{"key":"S0022481200017722_ref016","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1989-0955605-X"},{"key":"S0022481200017722_ref008","first-page":"255","volume":"49","author":"Kechris","year":"1984","journal-title":"The axiom of determinacy implies dependent choices in L[\u211d]"},{"key":"S0022481200017722_ref007","first-page":"99","volume-title":"Lecture notes in mathematics","author":"Kanamori","year":"1978"},{"key":"S0022481200017722_ref005","first-page":"41","article-title":"Regular cardinals in models of ZF","volume":"290","author":"Gitik","year":"1985","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200017722_ref006","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200017722_ref013","volume-title":"Lecture notes in mathematics","author":"Kleinberg","year":"1977"},{"key":"S0022481200017722_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02772571"},{"key":"S0022481200017722_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90031-1"},{"key":"S0022481200017722_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760939"},{"key":"S0022481200017722_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0090233"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017722","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T15:06:55Z","timestamp":1557760015000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017722\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["S0022481200017722"],"URL":"https:\/\/doi.org\/10.2307\/2275606","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}