{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T06:11:05Z","timestamp":1696486265503},"reference-count":13,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2016,4,21]],"date-time":"2016-04-21T00:00:00Z","timestamp":1461196800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"DFG-NWO cooperation","award":["1353\/5-1"],"award-info":[{"award-number":["1353\/5-1"]}]},{"name":"Hausdorff Center for Mathematics of the University of Bonn"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2016,5]]},"abstract":"<jats:p>Using the analysis developed in our earlier paper <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"#malq201400050-bib-0005\" \/>, we show that every uncountable cardinal in Gitik's model of <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"#malq201400050-bib-0008\" \/> in which all uncountable cardinals are singular is almost Ramsey and is also a Rowbottom cardinal carrying a Rowbottom filter. We assume that the model of <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"#malq201400050-bib-0008\" \/> is constructed from a proper class of strongly compact cardinals, each of which is a limit of measurable cardinals. Our work consequently reduces the best previously known upper bound in consistency strength for the theory <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400050-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400050:malq201400050-math-0001\" \/> + \u201cAll uncountable cardinals are singular\u201d + \u201cEvery uncountable cardinal is both almost Ramsey and a Rowbottom cardinal carrying a Rowbottom filter\u201d.<\/jats:p>","DOI":"10.1002\/malq.201400050","type":"journal-article","created":{"date-parts":[[2016,4,22]],"date-time":"2016-04-22T00:52:07Z","timestamp":1461286327000},"page":"225-231","source":"Crossref","is-referenced-by-count":1,"title":["All uncountable cardinals in the Gitik model are almost Ramsey and carry Rowbottom filters"],"prefix":"10.1002","volume":"62","author":[{"given":"Arthur W.","family":"Apter","sequence":"first","affiliation":[{"name":"Department of Mathematics Baruch College of CUNY New York New York 10010 United States of America"},{"name":"CUNY Graduate Center Mathematics  365 Fifth Avenue, New York New York 10016 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioanna M.","family":"Dimitriou","sequence":"additional","affiliation":[{"name":"Mathematisches Institut Rheinische Friedrich\u2010Wilhelms\u2010Universit\u00e4t Bonn  Endenicher Allee 60 53115 Bonn Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Koepke","sequence":"additional","affiliation":[{"name":"Mathematisches Institut Rheinische Friedrich\u2010Wilhelms\u2010Universit\u00e4t Bonn  Endenicher Allee 60 53115 Bonn Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2016,4,21]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02774081"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01269948"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.2307\/2586593"},{"key":"e_1_2_5_5_1","doi-asserted-by":"publisher","DOI":"10.2307\/2695085"},{"key":"e_1_2_5_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201110007"},{"key":"e_1_2_5_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-008-0107-1"},{"key":"e_1_2_5_8_1","doi-asserted-by":"crossref","first-page":"43","DOI":"10.4064\/fm-71-1-43-62","article-title":"Comparison of the axioms of local and universal choice","volume":"71","author":"Felgner U.","year":"1971","journal-title":"Fundam. 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