{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T08:13:09Z","timestamp":1772179989539,"version":"3.50.1"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2002,5]]},"abstract":"<jats:p>We show that every \u2135<jats:sub>\u03b1<\/jats:sub>(\u03b1&lt;\u03c9<jats:sub>1<\/jats:sub>) can be characterized by the Scott sentence of some countable model; moreover there is a countable structure whose Scott sentence characterizes \u2135<jats:sub>1<\/jats:sub>but whose automorphism group fails the topological Vaught conjecture on analytic sets.<\/jats:p><jats:p>We obtain some partial information on Ulm type dichotomy theorems for the automorphism group of Knight's model.<\/jats:p>","DOI":"10.1142\/s0219061302000084","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:07:52Z","timestamp":1027768072000},"page":"113-144","source":"Crossref","is-referenced-by-count":16,"title":["KNIGHT'S MODEL, ITS AUTOMORPHISM GROUP, AND CHARACTERIZING THE UNCOUNTABLE CARDINALS"],"prefix":"10.1142","volume":"02","author":[{"given":"GREG","family":"HJORTH","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-98-00258-6"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.2307\/2586718"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1990-1057041-5"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.2307\/2275888"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-00-00349-0"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02810686"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.2307\/2272318"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.2307\/2273623"},{"key":"p_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4064\/fm-159-1-1-50","volume":"159","author":"Shelah S.","year":"1999","journal-title":"Fund. Math."}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061302000084","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,5]],"date-time":"2020-03-05T04:57:00Z","timestamp":1583384220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061302000084"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,5]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2002,5]]}},"alternative-id":["10.1142\/S0219061302000084"],"URL":"https:\/\/doi.org\/10.1142\/s0219061302000084","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,5]]}}}