{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T09:22:16Z","timestamp":1648891336831},"reference-count":6,"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":12885,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1978,12]]},"abstract":"<jats:p>Since A. Robinson introduced the classes of existentially complete and generic models, conditions which were interesting for elementary classes were considered for these classes. In [6] H. Simmons showed that with the natural definitions there are prime and saturated existentially complete models and these are very similar to their elementary counterparts which were introduced by Vaught [2, 2.3]. As Example 6 will show, there is a limit to the similarity\u2014there are theories which have exactly two existentially complete models.<\/jats:p><jats:p>In [6] H. Simmons considers the following list of properties, shows that each property implies the next one and asks whether any of them implies the previous one:<\/jats:p><jats:p>1.1. <jats:italic>T<\/jats:italic> is \u2135<jats:sub>0<\/jats:sub>-categorical.<\/jats:p><jats:p>1.2. <jats:italic>T<\/jats:italic> has an \u2135<jats:sub>0<\/jats:sub>-categorical model companion.<\/jats:p><jats:p>1.3. \u2223<jats:italic>E<\/jats:italic>\u2223 = 1.<\/jats:p><jats:p>1.4. \u2223<jats:italic>E<\/jats:italic>\u2223 &lt; <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049161_inline1\" \/>.<\/jats:p><jats:p>1.5. <jats:italic>T<\/jats:italic> has a countable \u2203-saturated model.<\/jats:p><jats:p>1.6. <jats:italic>T<\/jats:italic> has a \u2203-prime model.<\/jats:p><jats:p>1.7. Each universal formula is implied by a \u2203-atomic existential formula.<\/jats:p><jats:p>[The reader is referred to [1], [3], [4] and [6] for the definitions and background.<\/jats:p><jats:p>We only mention that <jats:italic>T<\/jats:italic> is always a countable theory. <jats:italic>All the models under discussion are countable<\/jats:italic>. Thus <jats:italic>E<\/jats:italic> is the class of countable existentially complete models and <jats:italic>F<\/jats:italic> and <jats:italic>G<\/jats:italic>, respectively, are the classes of countable finite and infinite generic models. For every class C,\u2223<jats:italic>C<\/jats:italic>\u2223 is the number of (countable) models in <jats:italic>C<\/jats:italic>.]<\/jats:p>","DOI":"10.2307\/2273504","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:48:57Z","timestamp":1146952137000},"page":"650-658","source":"Crossref","is-referenced-by-count":0,"title":["Examples in the theory of existential completeness"],"prefix":"10.1017","volume":"43","author":[{"given":"Joram","family":"Hirschfeld","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200049161_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)70851-6"},{"key":"S0022481200049161_ref006","first-page":"307","article-title":"Counting countable E.C. structures","volume":"18","author":"Simmons","year":"1975","journal-title":"Logique et Analyse"},{"key":"S0022481200049161_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0064082"},{"key":"S0022481200049161_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90008-2"},{"key":"S0022481200049161_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771574"},{"key":"S0022481200049161_ref002","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\/S0022481200049161","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T19:07:45Z","timestamp":1558984065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200049161\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,12]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1978,12]]}},"alternative-id":["S0022481200049161"],"URL":"https:\/\/doi.org\/10.2307\/2273504","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,12]]}}}