{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T05:22:07Z","timestamp":1776316927895,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642360381","type":"print"},{"value":"9783642360398","type":"electronic"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-36039-8_13","type":"book-chapter","created":{"date-parts":[[2012,12,21]],"date-time":"2012-12-21T08:54:23Z","timestamp":1356080063000},"page":"139-147","source":"Crossref","is-referenced-by-count":10,"title":["Moving Up and Down in the Generic Multiverse"],"prefix":"10.1007","author":[{"given":"Joel David","family":"Hamkins","sequence":"first","affiliation":[]},{"given":"Benedikt","family":"L\u00f6we","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"1-2","key":"13_CR1","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s11225-012-9393-z","volume":"100","author":"L. Esakia","year":"2012","unstructured":"Esakia, L., L\u00f6we, B.: Fatal Heyting algebras and forcing persistent sentences. Studia Logica\u00a0100(1-2), 163\u2013173 (2012)","journal-title":"Studia Logica"},{"key":"13_CR2","unstructured":"Friedman, S., Fuchino, S., Sakai, H.: On the set-generic multiverse (submitted, 2012)"},{"issue":"1","key":"13_CR3","doi-asserted-by":"publisher","first-page":"276","DOI":"10.2178\/jsl\/1208358754","volume":"73","author":"G. Fuchs","year":"2008","unstructured":"Fuchs, G.: Closed maximality principles: implications, separations and combinations. Journal of Symbolic Logic\u00a073(1), 276\u2013308 (2008)","journal-title":"Journal of Symbolic Logic"},{"issue":"3","key":"13_CR4","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.2178\/jsl\/1245158097","volume":"74","author":"G. Fuchs","year":"2009","unstructured":"Fuchs, G.: Combined maximality principles up to large cardinals. Journal of Symbolic Logic\u00a074(3), 1015\u20131046 (2009)","journal-title":"Journal of Symbolic Logic"},{"key":"13_CR5","unstructured":"Fuchs, G., Hamkins, J.D., Reitz, J.: Set-theoretic geology (submitted, 2011)"},{"issue":"2","key":"13_CR6","doi-asserted-by":"publisher","first-page":"527","DOI":"10.2178\/jsl\/1052669062","volume":"68","author":"J.D. Hamkins","year":"2003","unstructured":"Hamkins, J.D.: A simple maximality principle. Journal of Symbolic Logic\u00a068(2), 527\u2013550 (2003)","journal-title":"Journal of Symbolic Logic"},{"issue":"4","key":"13_CR7","first-page":"3160","volume":"2","author":"J.D. Hamkins","year":"2005","unstructured":"Hamkins, J.D.: The Ground Axiom. Oberwolfach Reports\u00a02(4), 3160\u20133162 (2005)","journal-title":"Oberwolfach Reports"},{"key":"13_CR8","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/978-3-540-92701-3_3","volume-title":"Logic and Its Applications","author":"J.D. Hamkins","year":"2009","unstructured":"Hamkins, J.D.: Some Second Order Set Theory. In: Ramanujam, R., Sarukkai, S. (eds.) ICLA 2009. LNCS (LNAI), vol.\u00a05378, pp. 36\u201350. Springer, Heidelberg (2009)"},{"key":"13_CR9","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1017\/S1755020311000359","volume":"5","author":"J.D. Hamkins","year":"2012","unstructured":"Hamkins, J.D.: The set-theoretic multiverse. Review of Symbolic Logic\u00a05, 416\u2013449 (2012), doi:10.1017\/S1755020311000359","journal-title":"Review of Symbolic Logic"},{"key":"13_CR10","unstructured":"Hamkins, J.D., Leibman, G., L\u00f6we, B.: Structural connections between a forcing class and its modal logic (submitted, 2012)"},{"issue":"4","key":"13_CR11","doi-asserted-by":"publisher","first-page":"1793","DOI":"10.1090\/S0002-9947-07-04297-3","volume":"360","author":"J.D. Hamkins","year":"2008","unstructured":"Hamkins, J.D., L\u00f6we, B.: The modal logic of forcing. Transactions of the American Mathematical Society\u00a0360(4), 1793\u20131817 (2008)","journal-title":"Transactions of the American Mathematical Society"},{"issue":"5","key":"13_CR12","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1002\/malq.200410045","volume":"51","author":"J.D. Hamkins","year":"2005","unstructured":"Hamkins, J.D., Woodin, W.H.: The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal. Mathematical Logic Quarterly\u00a051(5), 493\u2013498 (2005)","journal-title":"Mathematical Logic Quarterly"},{"key":"13_CR13","series-title":"Springer Monographs in Mathematics","volume-title":"Set Theory","author":"T. Jech","year":"2003","unstructured":"Jech, T.: Set Theory, 3rd edn. Springer Monographs in Mathematics. Springer, Heidelberg (2003)","edition":"3"},{"issue":"1-3","key":"13_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.apal.2007.07.002","volume":"149","author":"R. Laver","year":"2007","unstructured":"Laver, R.: Certain very large cardinals are not created in small forcing extensions. Annals of Pure and Applied Logic\u00a0149(1-3), 1\u20136 (2007)","journal-title":"Annals of Pure and Applied Logic"},{"key":"13_CR15","unstructured":"Leibman, G.: Consistency strengths of modified maximality principles. PhD thesis, City University of New York (2004)"},{"issue":"2","key":"13_CR16","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1215\/00294527-2010-011","volume":"51","author":"G. Leibman","year":"2010","unstructured":"Leibman, G.: The consistency strength of \n                    \n                      \n                    \n                    ${\\rm MP}_{\\rm CCC}(\\Bbb R)$\n                  . Notre Dame Journal of Formal Logic\u00a051(2), 181\u2013193 (2010)","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"13_CR17","unstructured":"Reitz, J.: The Ground Axiom. PhD thesis, City University of New York (September 2006)"},{"issue":"4","key":"13_CR18","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.2178\/jsl\/1203350787","volume":"72","author":"J. Reitz","year":"2007","unstructured":"Reitz, J.: The Ground Axiom. Journal of Symbolic Logic\u00a072(4), 1299\u20131317 (2007)","journal-title":"Journal of Symbolic Logic"},{"key":"13_CR19","unstructured":"Rittberg, C.J.: The modal logic of forcing. Master\u2019s thesis, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster (2010)"},{"key":"13_CR20","series-title":"Synthese Library","volume-title":"The logic of time. A model-theoretic investigation into the varieties of temporal ontology and temporal discourse","author":"J.F.A.K. Benthem van","year":"1983","unstructured":"van Benthem, J.F.A.K.: The logic of time. A model-theoretic investigation into the varieties of temporal ontology and temporal discourse. Synthese Library, vol.\u00a0156. D. Reidel Publishing Co., Dordrecht (1983)"},{"key":"13_CR21","unstructured":"Woodin, W.H.: The continuum hypothesis, the generic multiverse of sets, and the \u03c9 conjecture (2009) (preprint)"}],"container-title":["Lecture Notes in Computer Science","Logic and Its Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-36039-8_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T01:40:27Z","timestamp":1558316427000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-36039-8_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642360381","9783642360398"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-36039-8_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}