{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T11:16:31Z","timestamp":1698491791681},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3603,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1997,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that weakly compact cardinals are the smallest large cardinals <jats:italic>k<\/jats:italic> where <jats:italic>k<\/jats:italic><jats:sup>+<\/jats:sup> &lt; <jats:italic>k<\/jats:italic><jats:sup>+<\/jats:sup> is impossible provided 0<jats:sup>#<\/jats:sup> does not exist. We also show that if <jats:italic>k<\/jats:italic><jats:sup>+<\/jats:sup><jats:sup>Kc<\/jats:sup> &lt; <jats:italic>k<\/jats:italic><jats:sup>+<\/jats:sup> for some <jats:italic>k<\/jats:italic> being weakly compact (where K<jats:sup>c<\/jats:sup> is the countably complete core model below one strong cardinal), then there is a transitive set M with M \u22a8 ZFC + \u201cthere is a strong cardinal\u201d.<\/jats:p>","DOI":"10.1002\/malq.19970430103","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T15:25:34Z","timestamp":1180538734000},"page":"22-28","source":"Crossref","is-referenced-by-count":1,"title":["Weak Covering at Large Cardinals"],"prefix":"10.1002","volume":"43","author":[{"given":"Ralf \u2010 Dieter","family":"Schindler","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21723-8"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274692"},{"key":"e_1_2_1_4_2","volume-title":"Set Theory","author":"Jech T.","year":"1978"},{"key":"e_1_2_1_5_2","unstructured":"Jensen R. B. The core model for non \u2010 overlapping extender sequences. Handwritten Notes."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0103104"},{"key":"e_1_2_1_7_2","volume-title":"Set Theory","author":"Kunen K.","year":"1980"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21903-4"},{"key":"e_1_2_1_9_2","unstructured":"Schimmerling E. Successors of weakly compact cardinals. Preprint1995."},{"key":"e_1_2_1_10_2","unstructured":"Schindler R.\u2010D. The core model up to one strong cardinal. Ph.D. Thesis Bonn1996."},{"key":"e_1_2_1_11_2","unstructured":"Steel J. The core model iterability problem. Preprint."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19970430103","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19970430103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T10:38:37Z","timestamp":1698489517000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19970430103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1997,1]]}},"alternative-id":["10.1002\/malq.19970430103"],"URL":"https:\/\/doi.org\/10.1002\/malq.19970430103","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}