{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T20:45:20Z","timestamp":1648932320878},"reference-count":4,"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":11699,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,3]]},"abstract":"<jats:p>Supercompactness is usually defined in terms of the existence of certain ultrafilters. By the well-known procedure of taking ultrapowers of <jats:italic>V<\/jats:italic> (the universe of sets) and transitive collapses, one obtains transitive inner models of <jats:italic>V<\/jats:italic> and corresponding elementary embeddings from <jats:italic>V<\/jats:italic> into these inner models. These embeddings have been studied extensively (see, e.g. [3] or [4]). We investigate the action of these embeddings on cardinals. In particular, we establish a characterization, based upon cofinality, of which cardinals are fixed by these embeddings.<\/jats:p>","DOI":"10.2307\/2273383","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:58:32Z","timestamp":1146952712000},"page":"84-88","source":"Crossref","is-referenced-by-count":0,"title":["Supercompact cardinals, elementary embeddings and fixed points"],"prefix":"10.1017","volume":"47","author":[{"given":"Julius B.","family":"Barbanel","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200044728_ref001","unstructured":"Barbanel J. B. , Results on supercompact cardinals, Ph.D. Thesis, State University of New York at Buffalo, 1979."},{"key":"S0022481200044728_ref002","unstructured":"Magidor M. , Private communication."},{"key":"S0022481200044728_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90031-1"},{"key":"S0022481200044728_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/025\/0379200"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200044728","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T21:43:01Z","timestamp":1558734181000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200044728\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,3]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,3]]}},"alternative-id":["S0022481200044728"],"URL":"https:\/\/doi.org\/10.2307\/2273383","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,3]]}}}