{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T17:52:12Z","timestamp":1711993932223},"reference-count":15,"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":1653,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,9]]},"abstract":"Abstract<\/jats:title>Let L<\/jats:italic>[E<\/jats:italic>] be an iterable tame extender model. We analyze to which extent L<\/jats:italic>[E<\/jats:italic>] knows fragments of its own iteration strategy. Specifically, we prove that inside L<\/jats:italic>[E<\/jats:italic>], for every cardinal \u03ba<\/jats:italic> which is not a limit of Woodin cardinals there is some cutpoint t<\/jats:italic> < \u03ba<\/jats:italic> such that J<\/jats:italic>\u03ba<\/jats:italic><\/jats:sub>[E<\/jats:italic>] is iterable above t<\/jats:italic> with respect to iteration trees of length less than \u03ba<\/jats:italic>.<\/jats:p>As an application we show L<\/jats:italic>[E<\/jats:italic>] to be a model of the following two cardinals versions of the diamond principle. If \u03bb<\/jats:italic> > \u03ba<\/jats:italic> > \u03c9<\/jats:italic>1<\/jats:sub> are cardinals, then holds true, and if in addition \u03bb<\/jats:italic> is regular, then holds true.<\/jats:p>","DOI":"10.2178\/jsl\/1245158084","type":"journal-article","created":{"date-parts":[[2009,6,16]],"date-time":"2009-06-16T09:16:09Z","timestamp":1245143769000},"page":"751-779","source":"Crossref","is-referenced-by-count":12,"title":["The self-iterability of L<\/i>[E<\/i>]"],"prefix":"10.1017","volume":"74","author":[{"given":"Ralf","family":"Schindler","sequence":"first","affiliation":[]},{"given":"John","family":"Steel","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003297_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02764635"},{"key":"S0022481200003297_ref008","author":"Schindler","journal-title":"Core models in the presence of Woodin cardinals"},{"key":"S0022481200003297_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0098503"},{"key":"S0022481200003297_ref012","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546488.011"},{"key":"S0022481200003297_ref013","volume-title":"Handbook of set theory","author":"Steel"},{"key":"S0022481200003297_ref011","first-page":"1197","volume":"67","author":"Steel","year":"2002","journal-title":"Core models with more Woodin cardinals"},{"key":"S0022481200003297_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(96)00032-2"},{"key":"S0022481200003297_ref007","first-page":"371","volume":"69","author":"Mitchell","year":"2004","journal-title":"A universal extender model without large cardinals in V"},{"key":"S0022481200003297_ref003","volume":"II","author":"Kanamori","journal-title":"The higher infinite"},{"key":"S0022481200003297_ref005","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.1995.v2.n5.a6"},{"key":"S0022481200003297_ref015","doi-asserted-by":"publisher","DOI":"10.1515\/9783110857818"},{"key":"S0022481200003297_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22485-4"},{"key":"S0022481200003297_ref014","unstructured":"Steel J. , in preparation."},{"key":"S0022481200003297_ref004","unstructured":"Kunen K. , Set theory. An introduction to independence proofs."},{"key":"S0022481200003297_ref002","unstructured":"Jensen R. , Some combinatorial properties of L and V, handwritten notes."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003297","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T07:24:16Z","timestamp":1556609056000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003297\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["S0022481200003297"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1245158084","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}