{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T11:51:24Z","timestamp":1649073084607},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T00:00:00Z","timestamp":1605225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2021,3]]},"abstract":"Abstract<\/jats:title>This paper establishes a conjecture of Steel [7] regarding the structure of elementary embeddings from a level of the cumulative hierarchy into itself. Steel\u2019s question is related to the Mitchell order on these embeddings, studied in [5] and [7]. Although this order is known to be illfounded, Steel conjectured that it has certain large wellfounded suborders, which is what we establish. The proof relies on a simple and general analysis of the much broader class of extender embeddings and a variant of the Mitchell order called the internal relation.<\/jats:p>","DOI":"10.1017\/jsl.2020.65","type":"journal-article","created":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T07:25:28Z","timestamp":1605252328000},"page":"137-147","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["RANK-TO-RANK EMBEDDINGS AND STEEL\u2019S CONJECTURE"],"prefix":"10.1017","volume":"86","author":[{"given":"GABRIEL","family":"GOLDBERG","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2020,11,13]]},"reference":[{"key":"S0022481220000651_r3","first-page":"407","article-title":"Elementary embeddings and infinitary combinatorics","volume":"36","author":"Kunen","year":"1971","journal-title":"Journal"},{"key":"S0022481220000651_r5","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(01)00103-8"},{"key":"S0022481220000651_r7","first-page":"931","article-title":"The well-foundedness of the Mitchell order","volume":"58","author":"Steel","year":"1993","journal-title":"Journal"},{"key":"S0022481220000651_r6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_20"},{"key":"S0022481220000651_r1","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/752\/15131"},{"key":"S0022481220000651_r2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90018-6"},{"key":"S0022481220000651_r4","first-page":"57","article-title":"Sets constructible from sequences of ultrafilters","volume":"39","author":"Mitchell","year":"1974","journal-title":"Journal"},{"key":"S0022481220000651_r8","doi-asserted-by":"publisher","DOI":"10.1515\/9783110857818"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481220000651","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T11:04:04Z","timestamp":1625742244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481220000651\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,13]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["S0022481220000651"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2020.65","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,13]]},"assertion":[{"value":"\u00a9 The Association for Symbolic Logic 2020","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}