{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:20:06Z","timestamp":1773231606314,"version":"3.50.1"},"reference-count":22,"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":11424,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that the statement \u201cFor every pair <jats:italic>A, B<\/jats:italic>, stationary subsets of <jats:italic>\u03c9<\/jats:italic><jats:sub>2<\/jats:sub>, composed of points of cofinality <jats:italic>\u03c9<\/jats:italic>, there exists an ordinal <jats:italic>\u03b1<\/jats:italic> such that both <jats:italic>A<\/jats:italic> \u2229 <jats:italic>\u03b1<\/jats:italic> and <jats:italic>B<\/jats:italic> \u2229 <jats:italic>\u03b1<\/jats:italic> are stationary subsets of <jats:italic>\u03b1<\/jats:italic> is equiconsistent with the existence of weakly compact cardinal. (This completes results of Baumgartner and Harrington and Shelah.)<\/jats:p><jats:p>We also prove, assuming the existence of infinitely many supercompact cardinals, the statement \u201cEvery stationary subset of <jats:italic>\u03c9<\/jats:italic><jats:sub><jats:italic>\u03c9+1<\/jats:italic><\/jats:sub> has a stationary initial segment.\u201d<\/jats:p>","DOI":"10.2307\/2273097","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:01:43Z","timestamp":1146952903000},"page":"755-771","source":"Crossref","is-referenced-by-count":84,"title":["Reflecting stationary sets"],"prefix":"10.1017","volume":"47","author":[{"given":"Menachem","family":"Magidor","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200043656_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757993"},{"key":"S0022481200043656_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90001-0"},{"key":"S0022481200043656_ref014","first-page":"65","volume":"43","author":"Kunen","year":"1978","journal-title":"Saturated ideals"},{"key":"S0022481200043656_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/1970860"},{"key":"S0022481200043656_ref008","unstructured":"Harrington L. and Shelah S. , Two equiconsistency results (to appear)."},{"key":"S0022481200043656_ref005","unstructured":"Dodd T. and Jensen R. , The core model, mimeographed notes, 1976."},{"key":"S0022481200043656_ref003","first-page":"251","volume":"45","author":"Beller","year":"1980","journal-title":"A strengthening of Jensen's \u25a1 principles"},{"key":"S0022481200043656_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761994"},{"key":"S0022481200043656_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(76)90001-2"},{"key":"S0022481200043656_ref009","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200043656_ref012","first-page":"99","volume-title":"Higher set theory, Lecture Notes in Mathematics","volume":"699","author":"Kanamori"},{"key":"S0022481200043656_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761379"},{"key":"S0022481200043656_ref010","first-page":"1","volume":"45","author":"Jech","year":"1980","journal-title":"Precipitous ideals"},{"key":"S0022481200043656_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90001-5"},{"key":"S0022481200043656_ref002","volume-title":"Cambridge Summer School of Set Theory","author":"Baumgartner","year":"1978"},{"key":"S0022481200043656_ref006","first-page":"93","article-title":"A partition calculus in set theory","volume":"62","author":"Erd\u00f6s","year":"1965","journal-title":"Bulletin of the American Mathematical Society"},{"key":"S0022481200043656_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/1971037"},{"key":"S0022481200043656_ref007","first-page":"139","article-title":"Eine Bemerkung zur Theorie der regresiven Funktionen","volume":"17","author":"Fodor","year":"1956","journal-title":"Acta Scientiarum Mathematicarum (Szeged)"},{"key":"S0022481200043656_ref019","doi-asserted-by":"publisher","DOI":"10.2307\/1970696"},{"key":"S0022481200043656_ref020","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90031-1"},{"key":"S0022481200043656_ref022","first-page":"75","volume":"40","author":"Prikry","year":"1975","journal-title":"On partitions into stationary sets"},{"key":"S0022481200043656_ref013","volume-title":"Model theory for infinitary logic","author":"Keisler","year":"1971"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200043656","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T20:18:12Z","timestamp":1558729092000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200043656\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["S0022481200043656"],"URL":"https:\/\/doi.org\/10.2307\/2273097","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}