{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T06:56:16Z","timestamp":1760424976277},"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":1562,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that if <jats:italic>\u03bc<\/jats:italic> is a regular cardinal and \u2119 is a <jats:italic>\u03bc<\/jats:italic>-centered forcing poset, then \u2119 forces that (<jats:italic>I<\/jats:italic>[<jats:italic>\u03bc<\/jats:italic><jats:sup>++<\/jats:sup>[)<jats:sup>V<\/jats:sup> generates <jats:italic>I<\/jats:italic>[<jats:italic>\u03bc<\/jats:italic><jats:sup>++<\/jats:sup>] modulo clubs. Using this result, we construct models in which the approachability property fails at the successor of a singular cardinal. We also construct models in which the properties of being internally club and internally approachable are distinct for sets of size the successor of a singular cardinal.<\/jats:p>","DOI":"10.2178\/jsl\/1254748688","type":"journal-article","created":{"date-parts":[[2009,10,5]],"date-time":"2009-10-05T17:05:40Z","timestamp":1254762340000},"page":"1211-1224","source":"Crossref","is-referenced-by-count":7,"title":["Approachability at the second successor of a singular cardinal"],"prefix":"10.1017","volume":"74","author":[{"given":"Moti","family":"Gitik","sequence":"first","affiliation":[]},{"given":"John","family":"Krueger","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003121_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200710080"},{"key":"S0022481200003121_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22400-7"},{"key":"S0022481200003121_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-04-03445-2"},{"key":"S0022481200003121_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90017-4"},{"key":"S0022481200003121_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761175"},{"key":"S0022481200003121_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759779"},{"key":"S0022481200003121_ref001","first-page":"159","volume-title":"Surveys in set theory","author":"Baumgartner","year":"1983"},{"key":"S0022481200003121_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2007.01.007"},{"key":"S0022481200003121_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BF01370693"},{"key":"S0022481200003121_ref015","first-page":"357","volume-title":"Logic colloquium 78","author":"Shelah","year":"1979"},{"key":"S0022481200003121_ref002","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1125409326"},{"key":"S0022481200003121_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/2944324"},{"key":"S0022481200003121_ref008","doi-asserted-by":"publisher","DOI":"10.4064\/fm201-2-2"},{"key":"S0022481200003121_ref012","doi-asserted-by":"publisher","DOI":"10.4064\/fm-99-1-61-71"},{"key":"S0022481200003121_ref009","volume-title":"Annals of Pure and Applied Logic","author":"Krueger"},{"key":"S0022481200003121_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(82)90023-7"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003121","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,29]],"date-time":"2019-04-29T22:35:15Z","timestamp":1556577315000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003121\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["S0022481200003121"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1254748688","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]}}}