{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:52:47Z","timestamp":1759146767696},"reference-count":12,"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":2658,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let 0 &lt; <jats:italic>n<\/jats:italic> &lt; \u03c9. If there are <jats:italic>n<\/jats:italic> Woodin cardinals and a measurable cardinal above, but <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005703_inline1\" \/> doesn't exist, then the core model <jats:italic>K<\/jats:italic> exists in a sense made precise. An Iterability Inheritance Hypothesis is isolated which is shown to imply an optimal correctness result for <jats:italic>K<\/jats:italic>.<\/jats:p>","DOI":"10.2178\/jsl\/1164060449","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:24:03Z","timestamp":1198081443000},"page":"1145-1154","source":"Crossref","is-referenced-by-count":2,"title":["Core models in the presence of Woodin cardinals"],"prefix":"10.1017","volume":"71","author":[{"given":"Ralf","family":"Schindler","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200005703_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22485-4"},{"key":"S0022481200005703_ref010","first-page":"1197","volume":"67","author":"Steel","year":"2002","journal-title":"Core models with more Woodin cardinals"},{"key":"S0022481200005703_ref007","unstructured":"Schindler R. and Steel J. , The self-iterability of L[E], in preparation."},{"key":"S0022481200005703_ref005","first-page":"241","volume-title":"Iterates of the core model","volume":"71","author":"Schindler","year":"2006"},{"key":"S0022481200005703_ref006","unstructured":"Schindler R. and Steel J. , List of open problems in inner model theory, available at www.mathl.uni-muenster.de\/logik\/org\/staff\/rds\/list.html."},{"key":"S0022481200005703_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02411-3"},{"key":"S0022481200005703_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21903-4"},{"key":"S0022481200005703_ref001","first-page":"371","volume":"69","author":"Mitchell","year":"2004","journal-title":"Kc without large cardinals in V"},{"key":"S0022481200005703_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00021-T"},{"key":"S0022481200005703_ref011","unstructured":"Steel J. , private communication."},{"key":"S0022481200005703_ref012","unstructured":"Woodin W. H. , private communication."},{"key":"S0022481200005703_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/421159"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200005703","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T19:29:18Z","timestamp":1556825358000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200005703\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["S0022481200005703"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1164060449","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12]]}}}