{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T23:38:17Z","timestamp":1706053097452},"reference-count":9,"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":3845,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2003,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We strengthen a theorem of Gitik and Shelah [6] by showing that if \u03ba is either weakly inaccessible or the successor of a singular cardinal and<jats:italic>S<\/jats:italic>is a stationary subset of \u03ba such that<jats:italic>NS<\/jats:italic><jats:sub>\u03ba<\/jats:sub>\u21be<jats:italic>S<\/jats:italic>is saturated then \u03ba \u2216<jats:italic>S<\/jats:italic>is fat. Using this theorem we derive some results about the existence of fat stationary sets. We then strengthen some results due to Baumgartner and Taylor [2], showing in particular that if<jats:italic>I<\/jats:italic>is a<jats:italic>\u03bb<\/jats:italic><jats:sup>+++<\/jats:sup>-saturated normal ideal on<jats:italic>P<\/jats:italic><jats:sub>\u03ba<\/jats:sub><jats:italic>\u03bb<\/jats:italic>then the conditions of being<jats:italic>\u03bb<\/jats:italic><jats:sup>+<\/jats:sup>-preserving, weakly presaturated, and presaturated are equivalent for<jats:italic>I<\/jats:italic>.<\/jats:p>","DOI":"10.2178\/jsl\/1058448442","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:08:41Z","timestamp":1109797721000},"page":"837-845","source":"Crossref","is-referenced-by-count":3,"title":["Fat sets and saturated ideals"],"prefix":"10.1017","volume":"68","author":[{"given":"John","family":"Krueger","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200008550_ref002","first-page":"587","article-title":"Saturation properties of ideals in generic extensions II","volume":"271","author":"Baumgartner","year":"1982","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200008550_ref001","first-page":"643","volume":"48","author":"Abraham","year":"1983","journal-title":"Forcing closed unbounded sets"},{"key":"S0022481200008550_ref008","first-page":"755","volume":"47","author":"Magidor","year":"1982","journal-title":"Reflecting stationary sets"},{"key":"S0022481200008550_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03995-6"},{"key":"S0022481200008550_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02785581"},{"key":"S0022481200008550_ref009","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537854.001.0001","volume-title":"Cardinal arithmetic","author":"Shelah","year":"1994"},{"key":"S0022481200008550_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03702-7"},{"key":"S0022481200008550_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/1971415"},{"key":"S0022481200008550_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22400-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200008550","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T22:45:44Z","timestamp":1706049944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200008550\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,9]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,9]]}},"alternative-id":["S0022481200008550"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1058448442","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,9]]}}}