{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,13]],"date-time":"2023-10-13T05:40:34Z","timestamp":1697175634569},"reference-count":11,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2005,8,3]],"date-time":"2005-08-03T00:00:00Z","timestamp":1123027200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2005,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is known that there is a close relation between Prikry forcing and the iteration of ultrapowers: If <jats:italic>U<\/jats:italic> is a normal ultrafilter on a measurable cardinal <jats:italic>\u03ba<\/jats:italic> and \u3008<jats:italic>M<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, <jats:italic>j<\/jats:italic><jats:sub><jats:italic>m,n<\/jats:italic><\/jats:sub> | <jats:italic>m<\/jats:italic> \u2264 <jats:italic>n<\/jats:italic> \u2264 <jats:italic>\u03c9<\/jats:italic>\u3009 is the iteration of ultrapowers of <jats:italic>V<\/jats:italic> by <jats:italic>U<\/jats:italic>, then the sequence of critical points \u3008<jats:italic>j<\/jats:italic><jats:sub>0,<jats:italic>n<\/jats:italic><\/jats:sub>(<jats:italic>\u03ba<\/jats:italic>) | <jats:italic>n<\/jats:italic> \u2208 <jats:italic>\u03c9<\/jats:italic>\u3009 is a Prikry generic sequence over <jats:italic>M<jats:sub>\u03c9<\/jats:sub><\/jats:italic>. In this paper we generalize this for normal precipitous filters. (\u00a9 2005 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200410047","type":"journal-article","created":{"date-parts":[[2005,8,3]],"date-time":"2005-08-03T20:53:33Z","timestamp":1123102413000},"page":"507-523","source":"Crossref","is-referenced-by-count":0,"title":["Generalized Prikry forcing and iteration of generic ultrapowers"],"prefix":"10.1002","volume":"51","author":[{"given":"Hiroshi","family":"Sakai","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,8,3]]},"reference":[{"issue":"1","key":"e_1_2_1_2_2","first-page":"77","article-title":"Iterated ultrapower and Prikry's forcing","volume":"18","author":"Bukovsk\u00fd L.","year":"1977","journal-title":"Comment. Math. Univ. Carolinae"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90018-9"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2273541"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272827"},{"key":"e_1_2_1_6_2","unstructured":"A.Kanamori The Higher Infinite (Springer\u2010Verlag Berlin et al. 1994)"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-99-1-61-71"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700028755"},{"key":"e_1_2_1_9_2","first-page":"5","article-title":"Changing measurable into accessible cardinals","volume":"68","author":"Prikry K.","year":"1970","journal-title":"Dissertationes Mathematicae"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","unstructured":"S.Shelah Proper and Improper Forcing 2nd ed. (Springer\u2010Verlag Berlin et al. 1998).","DOI":"10.1007\/978-3-662-12831-2"},{"issue":"2","key":"e_1_2_1_11_2","first-page":"241","article-title":"Well\u2010founded iterated generic ultrapowers","volume":"6","author":"Takahashi J.","year":"1989","journal-title":"Kobe J. Math."},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"H.Woodin The Axiom of Determinacy Forcing Axioms and the Nonstationary Ideal. De Gruyter Series in Logic and its Applications 1 (Walter de Gruyter Berlin et al. 1999).","DOI":"10.1515\/9783110804737"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200410047","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200410047","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T10:58:14Z","timestamp":1697108294000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200410047"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8,3]]},"references-count":11,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2005,9]]}},"alternative-id":["10.1002\/malq.200410047"],"URL":"https:\/\/doi.org\/10.1002\/malq.200410047","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8,3]]}}}