{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T18:29:37Z","timestamp":1649010577113},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":15442,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1971,12]]},"abstract":"<jats:p>A prime model <jats:italic>O<\/jats:italic> of some complete theory <jats:italic>T<\/jats:italic> is a model which can be elementarily imbedded into any model of <jats:italic>T<\/jats:italic> (cf. Vaught [7, Introduction]). We are going to replace the assumption that <jats:italic>T<\/jats:italic> is complete and that the maps between the models of <jats:italic>T<\/jats:italic> are elementary imbeddings (elementary extensions) by more general conditions. <jats:italic>T<\/jats:italic> will always be a first order theory with identity and may have function symbols. The language <jats:italic>L(T)<\/jats:italic> of <jats:italic>T<\/jats:italic> will be denumerable. The maps between models will be so called <jats:italic>F<\/jats:italic>-maps, i.e. maps which preserve a certain set <jats:italic>F<\/jats:italic> of formulas of <jats:italic>L(T)<\/jats:italic> (cf. I.1, 2). Roughly speaking a generalized prime model of <jats:italic>T<\/jats:italic> is a denumerable model <jats:italic>O<\/jats:italic> which permits an <jats:italic>F<\/jats:italic>-map <jats:italic>O\u2192M<\/jats:italic> into any model <jats:italic>M<\/jats:italic> of <jats:italic>T<\/jats:italic>. Furthermore <jats:italic>O<\/jats:italic> has to be \u201cgenerated\u201d by formulas which belong to a certain subset <jats:italic>G<\/jats:italic> of <jats:italic>F<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2272463","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:11:57Z","timestamp":1146949917000},"page":"593-606","source":"Crossref","is-referenced-by-count":1,"title":["Generalized prime models"],"prefix":"10.1017","volume":"36","author":[{"given":"Robert","family":"Fittler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200081433_ref004","first-page":"517","article-title":"Free \u03a3-structures","volume":"135","author":"Gr\u00e4tzer","year":"1969","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200081433_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079383"},{"key":"S0022481200081433_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1963-10903-9"},{"key":"S0022481200081433_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(69)90101-X"},{"key":"S0022481200081433_ref005","volume-title":"Universal algebra","author":"Gr\u00e4tzer","year":"1968"},{"key":"S0022481200081433_ref007","first-page":"303","volume-title":"Infinitistic methods","author":"Vaught","year":"1961"},{"key":"S0022481200081433_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19680360304"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200081433","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T19:37:01Z","timestamp":1559331421000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200081433\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1971,12]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1971,12]]}},"alternative-id":["S0022481200081433"],"URL":"https:\/\/doi.org\/10.2307\/2272463","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1971,12]]}}}