{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T12:07:48Z","timestamp":1748866068001},"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":10968,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1984,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In an earlier paper we proved that a universal Horn class generated by finitely many finite structures has a model companion. If the language has only finitely many fundamental operations then the theory of the model companion admits a primitive recursive elimination of quantifiers and is primitive recursive. The theory of the model companion is \u2135<jats:sub>0<\/jats:sub>-categorical iff it is complete iff the universal Horn class has the joint embedding property iff the universal Horn class is generated by a single finite structure. In the last section we look at structure theorems for the model companions of universal Horn classes generated by functionally complete algebras, in particular for the cases of rings and groups.<\/jats:p>","DOI":"10.2307\/2274092","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:07:02Z","timestamp":1146938822000},"page":"68-74","source":"Crossref","is-referenced-by-count":10,"title":["Model companions for finitely generated universal Horn classes"],"prefix":"10.1017","volume":"49","author":[{"given":"Stanley","family":"Burris","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200033958_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8130-3"},{"key":"S0022481200033958_ref006","first-page":"289","article-title":"The first-order theory of N-colorable graphs","volume":"250","author":"Wheeler","year":"1979","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200033958_ref004","first-page":"245","volume-title":"Actes du Congr\u00e8s International des Math\u00e9maticiens (Nice, 1970)","volume":"1","author":"Robinson","year":"1971"},{"key":"S0022481200033958_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1979-0522263-8"},{"key":"S0022481200033958_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1965-0175971-0"},{"key":"S0022481200033958_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02485711"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200033958","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T17:26:36Z","timestamp":1558632396000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200033958\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,3]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1984,3]]}},"alternative-id":["S0022481200033958"],"URL":"https:\/\/doi.org\/10.2307\/2274092","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,3]]}}}