{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T03:46:20Z","timestamp":1648611980730},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1380,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present Woodin's proof that if there exists a measurable Woodin cardinal <jats:italic>\u03b4<\/jats:italic> then there is a forcing extension satisfying all <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002735_inline1\" \/> sentences <jats:italic>\u03d5<\/jats:italic> such that <jats:italic>CH<\/jats:italic> + \u03d5 holds in a forcing extension of <jats:italic>V<\/jats:italic> by a partial order in <jats:italic>V<jats:sub>\u03b4<\/jats:sub><\/jats:italic>. We also use some of the techniques from this proof to show that if there exists a stationary limit of stationary limits of Woodin cardinals, then in a homogeneous forcing extension there is an elementary embedding <jats:italic>j<\/jats:italic>: <jats:italic>V<\/jats:italic> \u2192 <jats:italic>M<\/jats:italic> with critical point <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002735_inline2\" \/> such that <jats:italic>M<\/jats:italic> is countably closed in the forcing extension.<\/jats:p>","DOI":"10.2178\/jsl\/1268917500","type":"journal-article","created":{"date-parts":[[2010,3,18]],"date-time":"2010-03-18T13:05:57Z","timestamp":1268917557000},"page":"711-727","source":"Crossref","is-referenced-by-count":1,"title":["Regular embeddings of the stationary tower and Woodin's  maximality theorem"],"prefix":"10.1017","volume":"75","author":[{"given":"Richard","family":"Ketchersid","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul B.","family":"Larson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jind\u0159ich","family":"Zapletal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002735_ref008","unstructured":"Schindler R. and Steel J. , The core model induction , book in preparation."},{"key":"S0022481200002735_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200610054"},{"key":"S0022481200002735_ref004","volume-title":"The higher infinite. Large cardinals in set theory from their beginnings","author":"Kanamori","year":"2003"},{"key":"S0022481200002735_ref001","first-page":"47","volume-title":"Set theory and its applications","volume":"17","author":"Farah","year":"2006"},{"key":"S0022481200002735_ref006","volume-title":"The stationary tower. Notes on a course by W. Hugh Woodin","volume":"32","author":"Larson","year":"2004"},{"key":"S0022481200002735_ref005","volume-title":"Set theory. An introduction to independence proofs","author":"Kunen","year":"1983"},{"key":"S0022481200002735_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-00-05347-8"},{"key":"S0022481200002735_ref003","volume-title":"Set theory","author":"Jech","year":"2003"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002735","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,28]],"date-time":"2019-04-28T19:37:53Z","timestamp":1556480273000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002735\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,6]]}},"alternative-id":["S0022481200002735"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1268917500","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}