{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T08:12:37Z","timestamp":1772179957946,"version":"3.50.1"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5671,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1998,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Strengthening a theorem of D. W. Kueker, this paper completely charaterizes which countable structures do not admit uncountable <jats:italic>L<\/jats:italic><jats:sub>\u03c91\u03c9<\/jats:sub>-elementarily equivalent models. In particular, it is shown that if the automorphism group of a countable structure M is abelian, or even just solvable, then there is no uncountable model of the Scott sentence of <jats:italic>M<\/jats:italic>. These results arise as part of a study of Polish groups with compatible left-invariant complete metrics.<\/jats:p>","DOI":"10.2307\/2586718","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:01:28Z","timestamp":1146938488000},"page":"891-896","source":"Crossref","is-referenced-by-count":13,"title":["On automorphism groups of countable structures"],"prefix":"10.1017","volume":"63","author":[{"given":"Su","family":"Gao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200014651_ref010","first-page":"1402","volume":"58","year":"1993","journal-title":"On the number of automorphisms of uncountable models"},{"key":"S0022481200014651_ref009","first-page":"301","volume":"46","year":"1981","journal-title":"An example concerning Scott heights"},{"key":"S0022481200014651_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079688"},{"key":"S0022481200014651_ref001","volume-title":"Admissible sets and structures: an approach to definability theory","year":"1975"},{"key":"S0022481200014651_ref006","volume-title":"Classical descriptive set thoery","year":"1995"},{"key":"S0022481200014651_ref005","volume-title":"Model theory","year":"1993"},{"key":"S0022481200014651_ref003","volume-title":"The descriptive set theory of Polish group actions","year":"1996"},{"key":"S0022481200014651_ref007","volume-title":"Model theory for infinitary logic","volume":"62","year":"1971"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200014651","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T20:21:36Z","timestamp":1557519696000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200014651\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,9]]}},"alternative-id":["S0022481200014651"],"URL":"https:\/\/doi.org\/10.2307\/2586718","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,9]]}}}