{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T13:24:35Z","timestamp":1693488275811},"reference-count":4,"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":15076,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1972,12]]},"abstract":"<jats:p>The notion of an almost strongly minimal theory was introduced in [1]. Such a theory is a particularly simple sort of <jats:bold>\u2135<\/jats:bold><jats:sub>1<\/jats:sub>-categorical theory. In [1] we characterized this simplicity in terms of the Stone space of models of <jats:italic>T<\/jats:italic>. Here, we characterize almost strongly minimal theories which are not <jats:bold>\u2135<\/jats:bold><jats:sub>0<\/jats:sub>-categorical in terms of D. M. R. Park's notion [4] of a theory with the strong elementary intersection property. In addition we prove a useful sufficient condition for an elementary theory to be an almost strongly minimal theory. Our notation is from [1] but this paper is independent of the results proved there. We do assume familiarity with \u00a71 and \u00a72 of [2].<\/jats:p><jats:p>In [4], Park defines a theory <jats:italic>T<\/jats:italic> to have the strong elementary intersection property (s.e.i.p.) if for each model <jats:italic>C<\/jats:italic> of <jats:italic>T<\/jats:italic> and each pair <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200078440_inline1\" \/> of elementary submodels of <jats:italic>C<\/jats:italic> either <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200078440_inline2\" \/> is an elementary submodel of <jats:italic>C. T<\/jats:italic> has the nontrivial strong elementary intersection property (n.s.e.i.p.) if for each triple <jats:italic>C<\/jats:italic>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200078440_inline1\" \/> as above <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200078440_inline3\" \/> Park proves the following two statements equivalent:<\/jats:p>","DOI":"10.2307\/2272409","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:19:43Z","timestamp":1146935983000},"page":"657-660","source":"Crossref","is-referenced-by-count":2,"title":["Almost strongly minimal theories. II"],"prefix":"10.1017","volume":"37","author":[{"given":"John T.","family":"Baldwin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200078440_ref002","first-page":"79","volume":"36","author":"Baldwin","year":"1971","journal-title":"On strongly minimal sets"},{"key":"S0022481200078440_ref001","first-page":"487","volume":"37","author":"Baldwin","year":"1972","journal-title":"Almost strongly minimal theories. I"},{"key":"S0022481200078440_ref004","unstructured":"Park D. M. R. , Set theoretic constructions in model theory, Doctoral Dissertation, Massachusetts Institute of Technology, Cambridge, Mass., 1964."},{"key":"S0022481200078440_ref003","first-page":"A","article-title":"A note on almost strongly minimal theories","volume":"19","author":"Makowsky","year":"1972","journal-title":"Notices of the American Mathematical Society"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200078440","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T16:33:09Z","timestamp":1559233989000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200078440\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1972,12]]},"references-count":4,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1972,12]]}},"alternative-id":["S0022481200078440"],"URL":"https:\/\/doi.org\/10.2307\/2272409","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1972,12]]}}}