{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T08:28:03Z","timestamp":1648801683106},"reference-count":9,"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":6585,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We follow [8] in asking when a set of ordinals <jats:italic>X<\/jats:italic> \u2286 <jats:italic>\u03b1<\/jats:italic> is a countable union of sets in <jats:italic>K<\/jats:italic>, the core model. We show that, analogously to <jats:italic>L<\/jats:italic>, an <jats:italic>X<\/jats:italic> closed under the canonical \u03a3<jats:sub>1<\/jats:sub> Skolem function for <jats:italic>K<\/jats:italic><jats:sub><jats:italic>\u03b1<\/jats:italic><\/jats:sub> can be so decomposed provided <jats:italic>K<\/jats:italic> is such that no <jats:italic>\u03c9<\/jats:italic>-closed filters are put on its measure sequence, but not otherwise. This proviso holds if there is no inner model of a weak Erd\u0151s-type property.<\/jats:p>","DOI":"10.2307\/2275612","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:57:36Z","timestamp":1146956256000},"page":"293-312","source":"Crossref","is-referenced-by-count":1,"title":["Countable unions of simple sets in the core model"],"prefix":"10.1017","volume":"61","author":[{"given":"P. D.","family":"Welch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017783_ref009","first-page":"854","volume":"53","author":"Walker","year":"1988","journal-title":"On the transversal hypothesis and the weak Kurepa hypothesis"},{"key":"S0022481200017783_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90030-4"},{"key":"S0022481200017783_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21723-8"},{"key":"S0022481200017783_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90047-P"},{"key":"S0022481200017783_ref006","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200017783_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1990-0939805-5"},{"key":"S0022481200017783_ref007","unstructured":"Jensen R. B. , The core model for measures of order zero, circulated manuscript, 1989."},{"key":"S0022481200017783_ref003","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600586"},{"key":"S0022481200017783_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90028-Z"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017783","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T19:07:16Z","timestamp":1557774436000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017783\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["S0022481200017783"],"URL":"https:\/\/doi.org\/10.2307\/2275612","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}