{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T12:58:11Z","timestamp":1648904291955},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12795,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The language <jats:italic>L<\/jats:italic><jats:sub><jats:italic>A<\/jats:italic><\/jats:sub>(\u2132) is formed by adding the quantifier \u2132<jats:italic>x<\/jats:italic>, \u201cfew <jats:italic>x<\/jats:italic>\u201d, to the infinitary logic <jats:italic>L<jats:sub>A<\/jats:sub><\/jats:italic> on an admissible set <jats:italic>A<\/jats:italic>. A complete axiomatization is obtained for models whose universe is the set of ordinals of <jats:italic>A<\/jats:italic> and where \u2132<jats:italic>x<\/jats:italic> is interpreted as there exist <jats:italic>A<\/jats:italic>-finitely many <jats:italic>x<\/jats:italic>. For well-behaved <jats:italic>A<\/jats:italic>, every consistent sentence has a model with an <jats:italic>A<\/jats:italic>-recursive diagram. A principal tool is forcing for <jats:italic>L<\/jats:italic><jats:sub><jats:italic>A<\/jats:italic><\/jats:sub>(\u2132).<\/jats:p>","DOI":"10.2307\/2273698","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:49:34Z","timestamp":1146952174000},"page":"15-28","source":"Crossref","is-referenced-by-count":5,"title":["<i>L<\/i><sub><i>A<\/i><\/sub>(\u2132)"],"prefix":"10.1017","volume":"44","author":[{"given":"Kim","family":"Bruce","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H. J.","family":"Keisler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048660_ref006","volume-title":"Model theory for infinitary logic","author":"Keisler","year":"1971"},{"key":"S0022481200048660_ref005","unstructured":"Keisler H. J. , LA(Q), mimeographed, 1970 (unpublished)."},{"key":"S0022481200048660_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0003-4843(78)80001-1"},{"key":"S0022481200048660_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/S0003-4843(70)80005-5"},{"key":"S0022481200048660_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-11035-5"},{"key":"S0022481200048660_ref003","volume-title":"Model theory","author":"Chang","year":"1973"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048660","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T21:56:59Z","timestamp":1558907819000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048660\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,3]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1979,3]]}},"alternative-id":["S0022481200048660"],"URL":"https:\/\/doi.org\/10.2307\/2273698","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,3]]}}}