{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T22:47:59Z","timestamp":1759963679983},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2008,5,31]],"date-time":"2008-05-31T00:00:00Z","timestamp":1212192000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2008,7]]},"DOI":"10.1007\/s00153-008-0072-8","type":"journal-article","created":{"date-parts":[[2008,5,30]],"date-time":"2008-05-30T08:23:29Z","timestamp":1212135809000},"page":"133-142","source":"Crossref","is-referenced-by-count":3,"title":["Universal indestructibility for degrees of supercompactness and strongly compact cardinals"],"prefix":"10.1007","volume":"47","author":[{"given":"Arthur W.","family":"Apter","sequence":"first","affiliation":[]},{"given":"Grigor","family":"Sargsyan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,5,31]]},"reference":[{"key":"72_CR1","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1007\/s001530200139","volume":"41","author":"A. Apter","year":"2002","unstructured":"Apter A.: Aspects of strong compactness, measurability, and indestructibility. Arch. Math. Log. 41, 705\u2013719 (2002)","journal-title":"Arch. Math. Log."},{"key":"72_CR2","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s00153-003-0181-3","volume":"42","author":"A. Apter","year":"2003","unstructured":"Apter A.: Some remarks on indestructibility and Hamkins\u2019 lottery preparation. Arch. Math. Log. 42, 717\u2013735 (2003)","journal-title":"Arch. Math. Log."},{"key":"72_CR3","doi-asserted-by":"crossref","first-page":"131","DOI":"10.4064\/ba53-2-2","volume":"53","author":"A. Apter","year":"2005","unstructured":"Apter A.: Universal indestructibility is consistent with two strongly compact cardinals. Bull. Pol. Acad. Sci. 53, 131\u2013135 (2005)","journal-title":"Bull. Pol. Acad. Sci."},{"key":"72_CR4","doi-asserted-by":"crossref","first-page":"1404","DOI":"10.2307\/2586658","volume":"63","author":"A. Apter","year":"1998","unstructured":"Apter A., Gitik M.: The least measurable can be strongly compact and indestructible. J. Symb. Log. 63, 1404\u20131412 (1998)","journal-title":"J. Symb. Log."},{"key":"72_CR5","doi-asserted-by":"crossref","first-page":"669","DOI":"10.2178\/jsl\/1052669070","volume":"68","author":"A. Apter","year":"2003","unstructured":"Apter A., Hamkins J.D.: Exactly controlling the non-supercompact strongly compact cardinals. J. Symb. Log. 68, 669\u2013688 (2003)","journal-title":"J. Symb. Log."},{"key":"72_CR6","first-page":"119","volume":"16","author":"A. Apter","year":"1999","unstructured":"Apter A., Hamkins J.D.: Universal indestructibility. Kobe J. Math. 16, 119\u2013130 (1999)","journal-title":"Kobe J. Math."},{"key":"72_CR7","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s00153-005-0316-9","volume":"45","author":"A. Apter","year":"2006","unstructured":"Apter A., Sargsyan G.: Identity crises and strong compactness III: Woodin cardinals. Arch. Math. Log. 45, 307\u2013322 (2006)","journal-title":"Arch. Math. Log."},{"key":"72_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1992-1041044-9","volume":"329","author":"J. Cummings","year":"1992","unstructured":"Cummings J.: A model in which GCH holds at successors but fails at limits. Trans. Am. Math. Soc. 329, 1\u201339 (1992)","journal-title":"Trans. Am. Math. Soc."},{"key":"72_CR9","doi-asserted-by":"crossref","unstructured":"Foreman, M.: More saturated ideals. In: Cabal Seminar 79\u201381. Lecture Notes in Mathematics, vol. 1019, pp. 1\u201327. Springer, Berlin (1983)","DOI":"10.1007\/BFb0071691"},{"key":"72_CR10","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF02773382","volume":"125","author":"J.D. Hamkins","year":"2001","unstructured":"Hamkins J.D.: Gap forcing. Isr. J. Math. 125, 237\u2013252 (2001)","journal-title":"Isr. J. Math."},{"key":"72_CR11","doi-asserted-by":"crossref","first-page":"264","DOI":"10.2307\/421092","volume":"5","author":"J.D. Hamkins","year":"1999","unstructured":"Hamkins J.D.: Gap forcing: generalizing the L\u00e9vy-Solovay theorem. Bull. Symb. Log. 5, 264\u2013272 (1999)","journal-title":"Bull. Symb. Log."},{"key":"72_CR12","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0168-0072(99)00010-X","volume":"101","author":"J.D. Hamkins","year":"2000","unstructured":"Hamkins J.D.: The lottery preparation. Ann. Pure Appl. Log. 101, 103\u2013146 (2000)","journal-title":"Ann. Pure Appl. Log."},{"key":"72_CR13","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/BF02761175","volume":"29","author":"R. Laver","year":"1978","unstructured":"Laver R.: Making the supercompactness of \u03ba indestructible under \u03ba-directed closed forcing. Isr. J. Math. 29, 385\u2013388 (1978)","journal-title":"Isr. J. Math."},{"key":"72_CR14","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1007\/BF02771612","volume":"5","author":"A. L\u00e9vy","year":"1967","unstructured":"L\u00e9vy A., Solovay R.: Measurable cardinals and the continuum hypothesis. Isr. J. Math. 5, 234\u2013248 (1967)","journal-title":"Isr. J. Math."}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-008-0072-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-008-0072-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-008-0072-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T15:36:42Z","timestamp":1558625802000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-008-0072-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5,31]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["72"],"URL":"https:\/\/doi.org\/10.1007\/s00153-008-0072-8","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5,31]]}}}