{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:15:03Z","timestamp":1778717703327,"version":"3.51.4"},"reference-count":11,"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":376,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Recently, Gitik, Kanovei and the first author proved that for a classical Prikry forcing extension the family of the intermediate models can be parametrized by <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000281_inline01\"\/>\/finite. By modifying the standard Prikry tree forcing we define a Prikry-type forcing which also singularizes a measurable cardinal but which is minimal, i.e., there are <jats:italic>no<\/jats:italic> intermediate models properly between the ground model and the generic extension. The proof relies on combining the rigidity of the tree structure with indiscernibility arguments resulting from the normality of the associated measures.<\/jats:p>","DOI":"10.2178\/jsl.7801060","type":"journal-article","created":{"date-parts":[[2013,1,23]],"date-time":"2013-01-23T09:38:23Z","timestamp":1358933903000},"page":"85-100","source":"Crossref","is-referenced-by-count":5,"title":["A minimal Prikry-type forcing for singularizing a measurable cardinal"],"prefix":"10.1017","volume":"78","author":[{"given":"Peter","family":"Koepke","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karen","family":"R\u00e4sch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philipp","family":"Schlicht","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200000281_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700028755"},{"key":"S0022481200000281_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90001-5"},{"key":"S0022481200000281_ref009","first-page":"1","article-title":"Changing measurable into accessible cardinals","volume":"68","author":"Prikry","year":"1970","journal-title":"Dissertationes Mathematicae"},{"key":"S0022481200000281_ref005","volume-title":"Set theory, revised and expanded","author":"Jech","year":"2006"},{"key":"S0022481200000281_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(82)90018-3"},{"key":"S0022481200000281_ref004","unstructured":"Gray C. W. , Iterated forcing from the strategic point of view, Ph.D. thesis, University of California, Berkeley, California, 1980."},{"key":"S0022481200000281_ref011","first-page":"58","volume-title":"Axiomatic set theory","volume":"XIII","author":"Sacks","year":"1971"},{"key":"S0022481200000281_ref010","unstructured":"R\u00e4sch Karen , Intermediate models of generic extensions by Prikry forcings, Master's thesis, Universit\u00e4t Bonn, 2010."},{"key":"S0022481200000281_ref006","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0168-0072(89)90016-X","article-title":"-Assets of reals","volume":"42","author":"Judah","year":"1989","journal-title":"Annals of Pure and Applied Logic"},{"key":"S0022481200000281_ref003","unstructured":"Gitik Moti , Kanovei Vladimir , and Koepke Peter , Intermediate models of Prikry generic extensions, preprint, 2010."},{"key":"S0022481200000281_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_17"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000281","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T15:11:38Z","timestamp":1556118698000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000281\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["S0022481200000281"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7801060","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3]]}}}