{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T09:11:49Z","timestamp":1696497109605},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2018,12]]},"abstract":"Abstract<\/jats:title>We explore the structural properties of the inner model L<\/jats:italic>(V<\/jats:italic>\u03b4+<\/jats:italic>1<\/jats:sub>) under the assumption that \u03b4<\/jats:italic> is a singular limit of Berkeley cardinals each of which is itself limit of extendible cardinals, lifting some of the main results of the theory of the axiom I0<\/jats:sub> to the level of Berkeley cardinals, the strongest known large cardinal axioms. Berkeley cardinals have been recently introduced in [1] and contradict the Axiom of Choice.1<\/jats:sup> In fact, our background theory will be ZF.<\/jats:p>","DOI":"10.1017\/jsl.2018.35","type":"journal-article","created":{"date-parts":[[2018,12,21]],"date-time":"2018-12-21T13:49:38Z","timestamp":1545400178000},"page":"1457-1476","source":"Crossref","is-referenced-by-count":1,"title":["BERKELEY CARDINALS AND THE STRUCTURE OF L(V\u03b4+1)"],"prefix":"10.1017","volume":"83","author":[{"given":"RAFFAELLA","family":"CUTOLO","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,12,21]]},"reference":[{"key":"S002248121800035X_ref3","year":"2017","journal-title":"Bollettino Dell\u2019Unione Matematica Italiana"},{"key":"S002248121800035X_ref8","doi-asserted-by":"publisher","DOI":"10.1142\/S021906131100102X"},{"key":"S002248121800035X_ref7","doi-asserted-by":"publisher","DOI":"10.1142\/S021906131000095X"},{"key":"S002248121800035X_ref2","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/690\/13870"},{"key":"S002248121800035X_ref5","volume-title":"The Higher Infinite: Large Cardinals in Set Theory From Their Beginnings","year":"2003"},{"key":"S002248121800035X_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-003-0204-0"},{"key":"S002248121800035X_ref6","first-page":"107","volume-title":"Cabal Seminar 79\u201381","year":"1983"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248121800035X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,12,21]],"date-time":"2018-12-21T13:49:53Z","timestamp":1545400193000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248121800035X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12]]},"references-count":7,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["S002248121800035X"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2018.35","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12]]}}}