{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T04:40:16Z","timestamp":1713415216976},"reference-count":12,"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":741,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let<jats:italic>A<\/jats:italic>be a non-empty set. A set<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000918_inline02\" \/>is said to be stationary in<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000918_inline03\" \/>if for every<jats:italic>f<\/jats:italic>: [<jats:italic>A<\/jats:italic>]<jats:sup>&lt;<jats:italic>\u03c9<\/jats:italic><\/jats:sup>\u2192<jats:italic>A<\/jats:italic>there exists<jats:italic>x<\/jats:italic>\u03f5<jats:italic>S<\/jats:italic>such that<jats:italic>x<\/jats:italic>\u2260<jats:italic>A<\/jats:italic>and<jats:italic>f<\/jats:italic>\u201c[<jats:italic>x<\/jats:italic>]<jats:sup>&lt;<jats:italic>\u03c9<\/jats:italic><\/jats:sup>\u2286<jats:italic>x<\/jats:italic>. In this paper we prove the following: For an uncountable cardinal \u03bb and a stationary set<jats:italic>S<\/jats:italic>in<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000918_inline04\" \/>, if there is a regular uncountable cardinal<jats:italic>\u03ba<\/jats:italic>\u2264 \u03bb such that {<jats:italic>x<\/jats:italic>\u03f5<jats:italic>S<\/jats:italic>:<jats:italic>x<\/jats:italic>\u2229<jats:italic>\u03ba<\/jats:italic>\u03f5<jats:italic>\u03ba<\/jats:italic>} is stationary, then<jats:italic>S<\/jats:italic>can be split into<jats:italic>\u03ba<\/jats:italic>disjoint stationary subsets.<\/jats:p>","DOI":"10.2178\/jsl\/1327068691","type":"journal-article","created":{"date-parts":[[2012,1,20]],"date-time":"2012-01-20T14:16:13Z","timestamp":1327068973000},"page":"49-62","source":"Crossref","is-referenced-by-count":1,"title":["Splitting stationary sets in"],"prefix":"10.1017","volume":"77","author":[{"given":"Toshimichi","family":"Usuba","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200000918_ref012","first-page":"397","volume-title":"Axiomatic set theory (Proceedings of the symposium on Pure Mathematics, Vol XIII, Part I, University of California, Los Angeles, California, 1967)","author":"Solovay","year":"1971"},{"key":"S0022481200000918_ref010","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537854.001.0001","volume-title":"Cardinal arithmetic","volume":"29","author":"Shelah","year":"1994"},{"key":"S0022481200000918_ref009","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/04220259"},{"key":"S0022481200000918_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(73)90014-4"},{"key":"S0022481200000918_ref005","first-page":"881","volume":"50","author":"Gitik","year":"1985","journal-title":"Nonsplitting subset P\u03ba(\u03ba+)"},{"key":"S0022481200000918_ref011","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2003.v10.n4.a8"},{"key":"S0022481200000918_ref002","unstructured":"[] Burke D. , Splitting stationary subsets of unpublished."},{"key":"S0022481200000918_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0819932-2"},{"key":"S0022481200000918_ref008","volume-title":"The stationary tower. Notes on a course by W. Hugh Woodin","volume":"32","author":"Larson","year":"2004"},{"key":"S0022481200000918_ref007","volume-title":"The higher infinite: Large cardinals in set theory from their beginnings","author":"Kanamori","year":"1994"},{"key":"S0022481200000918_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_15"},{"key":"S0022481200000918_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_14"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000918","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T04:19:34Z","timestamp":1713413974000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000918\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["S0022481200000918"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1327068691","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}