{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,13]],"date-time":"2023-10-13T08:10:33Z","timestamp":1697184633050},"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>For any ordinal <jats:italic>\u03b4<\/jats:italic>, let <jats:italic>\u03bb<jats:sub>\u03b4<\/jats:sub><\/jats:italic> be the least inaccessible cardinal above <jats:italic>\u03b4<\/jats:italic>. We force and construct a model in which the least supercompact cardinal <jats:italic>\u03ba<\/jats:italic> is indestructible under <jats:italic>\u03ba<\/jats:italic>\u2010directed closed forcing and in which every measurable cardinal <jats:italic>\u03b4<\/jats:italic> &lt; <jats:italic>\u03ba<\/jats:italic> is &lt; <jats:italic>\u03bb<jats:sub>\u03b4<\/jats:sub><\/jats:italic> strongly compact and has its &lt; <jats:italic>\u03bb<jats:sub>\u03b4<\/jats:sub><\/jats:italic> strong compactness indestructible under <jats:italic>\u03b4<\/jats:italic>\u2010directed closed forcing of rank less than <jats:italic>\u03bb<jats:sub>\u03b4<\/jats:sub><\/jats:italic>. In this model, <jats:italic>\u03ba<\/jats:italic> is also the least strongly compact cardinal. We also establish versions of this result in which <jats:italic>\u03ba<\/jats:italic> is the least strongly compact cardinal but is not supercompact. (\u00a9 2005 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200510004","type":"journal-article","created":{"date-parts":[[2005,8,3]],"date-time":"2005-08-03T22:20:52Z","timestamp":1123107652000},"page":"524-531","source":"Crossref","is-referenced-by-count":1,"title":["Universal partial indestructibility and strong compactness"],"prefix":"10.1002","volume":"51","author":[{"given":"Arthur W.","family":"Apter","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,8,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19970430316"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2695085"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2586658"},{"key":"e_1_2_1_5_2","first-page":"119","article-title":"Universal indestructibility","volume":"16","author":"Apter A.","year":"1999","journal-title":"Kobe J. Mathematics"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02782938"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2586746"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(99)00010-X"},{"key":"e_1_2_1_9_2","unstructured":"A.Kanamori The Higher Infinite (Springer\u2010Verlag Berlin et al. 1994)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761175"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(76)90024-3"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"R.Solovay Strongly compact cardinals and the GCH. In: Proceedings of the Tarski Symposium Proceedings of Symposia in Pure Mathematics 25 pp. 365\u2013372 (American Mathematical Society Providence 1974).","DOI":"10.1090\/pspum\/025\/0379200"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200510004","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200510004","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T10:58:40Z","timestamp":1697108320000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200510004"}},"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.200510004"],"URL":"https:\/\/doi.org\/10.1002\/malq.200510004","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]]}}}