{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:28:23Z","timestamp":1759847303912},"reference-count":9,"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":1653,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003273_inline1\" \/>be a finite relational language and<jats:italic>\u03b1<\/jats:italic>= (<jats:italic>\u03b1<jats:sub>R<\/jats:sub><\/jats:italic>:<jats:italic>R<\/jats:italic>\u2208<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003273_inline1\" \/>) a tuple with 0 &lt;<jats:italic>\u03b1<jats:sub>R<\/jats:sub><\/jats:italic>\u2264 1 for each<jats:italic>R<\/jats:italic>\u2208<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003273_inline1\" \/>. Consider a dimension function<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200003273_eqnU1\" \/><\/jats:disp-formula><\/jats:p><jats:p>where each<jats:italic>e<jats:sub>R<\/jats:sub>(A)<\/jats:italic>is the number of realizations of<jats:italic>R<\/jats:italic>in<jats:italic>A<\/jats:italic>. Let<jats:bold>K<\/jats:bold><jats:sub><jats:italic>\u03b1<\/jats:italic><\/jats:sub>be the class of finite structures<jats:italic>A<\/jats:italic>such that<jats:italic>\u03b4<jats:sub>\u03b1<\/jats:sub>(X)<\/jats:italic>\u2265 0 for any substructure<jats:italic>X<\/jats:italic>of<jats:italic>A<\/jats:italic>. We show that the theory of the generic model of<jats:bold>K<\/jats:bold><jats:sub><jats:italic>\u03b1<\/jats:italic><\/jats:sub>is AE-axiomatizable for any<jats:italic>\u03b1<\/jats:italic>.<\/jats:p>","DOI":"10.2178\/jsl\/1245158082","type":"journal-article","created":{"date-parts":[[2009,6,16]],"date-time":"2009-06-16T13:16:09Z","timestamp":1245158169000},"page":"721-733","source":"Crossref","is-referenced-by-count":3,"title":["On generic structures with a strong amalgamation property"],"prefix":"10.1017","volume":"74","author":[{"given":"Koichiro","family":"Ikeda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hirotaka","family":"Kikyo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akito","family":"Tsuboi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003273_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-97-01869-2"},{"key":"S0022481200003273_ref003","unstructured":"Hrushovski E. , A stable \u21350-categorical pseudoplane, preprint, 1988."},{"key":"S0022481200003273_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.06.006"},{"key":"S0022481200003273_ref004","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1074396310"},{"key":"S0022481200003273_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-007-0077-8"},{"key":"S0022481200003273_ref009","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1093\/oso\/9780198534686.003.0006","volume-title":"Automorphisms of first-order structures","author":"Wagner","year":"1994"},{"key":"S0022481200003273_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04538-1"},{"key":"S0022481200003273_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(95)00027-5"},{"key":"S0022481200003273_ref005","first-page":"75","article-title":"On predimensions of finite structures","volume":"1450","author":"Kikyo","year":"2005","journal-title":"Kokyuroku of RIMS in Kyoto University"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003273","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,14]],"date-time":"2024-03-14T17:00:46Z","timestamp":1710435646000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003273\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["S0022481200003273"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1245158082","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}