{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T22:39:47Z","timestamp":1648852787865},"reference-count":9,"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":7406,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1993,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, assuming large cardinals, we prove the consistency of the following:<\/jats:p><jats:p>Let <jats:italic>n<\/jats:italic> \u2208 <jats:italic>\u03c9<\/jats:italic> and <jats:italic>k<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>k<\/jats:italic><jats:sub>2<\/jats:sub> \u2264 <jats:italic>n<\/jats:italic>. Let <jats:italic>f<\/jats:italic>: <jats:italic>\u03c9<\/jats:italic> \u2192 {<jats:italic>k<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>k<\/jats:italic><jats:sub>2<\/jats:sub>} be such that for all <jats:italic>n<\/jats:italic><jats:sub>1<\/jats:sub> &lt; <jats:italic>n<\/jats:italic><jats:sub>2<\/jats:sub> \u2208 <jats:italic>f<\/jats:italic><jats:sup>\u22121<\/jats:sup>{<jats:italic>k<\/jats:italic><jats:sub>1<\/jats:sub>},<jats:italic>n<\/jats:italic><jats:sub>2<\/jats:sub> \u2212 <jats:italic>n<\/jats:italic><jats:sub>1<\/jats:sub> \u2265 4. Then the set<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200020557_eqnU1\" \/><\/jats:disp-formula><\/jats:p><jats:p>is stationary in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020557_inline2\" \/><\/jats:p><jats:p>The above is equivalent to the statement that for any structure on <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020557_inline3\" \/> on \u2135<jats:sub><jats:italic>\u03c9<\/jats:italic><\/jats:sub>, there is <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020557_inline4\" \/> \u227a <jats:italic>A<\/jats:italic> such that \u2223<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020557_inline4\" \/>\u2223 = <jats:italic>\u03c9<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> and for all <jats:italic>m<\/jats:italic> &gt; <jats:italic>n, cf<\/jats:italic>(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020557_inline4\" \/> \u2229 <jats:italic>\u03c9<\/jats:italic><jats:sub><jats:italic>m<\/jats:italic><\/jats:sub>) = <jats:italic>\u03c9<\/jats:italic><jats:sub><jats:italic>f(m)<\/jats:italic><\/jats:sub>.<\/jats:p>","DOI":"10.2307\/2275139","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:50:13Z","timestamp":1146955813000},"page":"1201-1218","source":"Crossref","is-referenced-by-count":4,"title":["Stationary subsets of [\u2135<sub><i>\u03c9<\/i><\/sub>]<sup>&lt;<i>\u03c9<sub>n<\/sub><\/i><\/sup>"],"prefix":"10.1017","volume":"58","author":[{"given":"Kecheng","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200020557_ref007","volume-title":"Set theory. An introduction to independence proofs","author":"Kunen","year":"1980"},{"key":"S0022481200020557_ref006","first-page":"65","volume":"43","author":"Kunen","year":"1978","journal-title":"Saturated ideals"},{"key":"S0022481200020557_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0103104"},{"key":"S0022481200020557_ref003","volume-title":"More saturated ideals","volume":"1019","author":"Foreman","year":"1983"},{"key":"S0022481200020557_ref002","first-page":"1","volume-title":"Surveys in set theory","author":"Baumgartner","year":"1983"},{"key":"S0022481200020557_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1982-0662045-X"},{"key":"S0022481200020557_ref009","first-page":"269","volume-title":"Proceedings of the International Congress of Mathematicians (Helsinki, 1978)","author":"Martin","year":"1980"},{"key":"S0022481200020557_ref008","volume-title":"Logic colloquium 1980 (Prague)","author":"Laver","year":"1982"},{"key":"S0022481200020557_ref001","unstructured":"Baumgartner J. , On the size of closed unbounded sets, manuscript."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200020557","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T21:03:49Z","timestamp":1557954229000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200020557\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,12]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1993,12]]}},"alternative-id":["S0022481200020557"],"URL":"https:\/\/doi.org\/10.2307\/2275139","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,12]]}}}