{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T20:49:39Z","timestamp":1648759779292},"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":11334,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1983,3]]},"abstract":"<jats:p>In this paper <jats:italic>T<\/jats:italic> will always be a countable \u2135<jats:sub>0<\/jats:sub>-stable theory, and in this introduction a model of <jats:italic>T<\/jats:italic> will mean a countable model.<\/jats:p><jats:p>One of the main notions we introduce is that of almost homogeneous model: we say that a model <jats:italic>M<\/jats:italic> of <jats:italic>T<\/jats:italic> is almost homogeneous if for all <jats:italic>\u0101<\/jats:italic> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200043498_inline1\" \/> finite sequences of elements in <jats:italic>M<\/jats:italic>, if the strong type of <jats:italic>\u0101<\/jats:italic> is the same as the strong type of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200043498_inline1\" \/> (i.e. for all equivalence relations <jats:italic>E<\/jats:italic>, definable over the empty set and with a finite number of equivalence classes, <jats:italic>\u0101<\/jats:italic> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200043498_inline1\" \/> are in the same equivalence class), then there is an automorphism of <jats:italic>M<\/jats:italic> taking <jats:italic>\u0101<\/jats:italic> to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200043498_inline1\" \/>. Although this is a weaker notion than homogeneity, these models have strong properties, and it can be seen easily that the Scott formula of any almost homogeneous model is in <jats:italic>L<\/jats:italic><jats:sub>1<\/jats:sub>. In fact, Pillay [Pi.] has shown that almost homogeneous models are characterized by the set of types they realize.<\/jats:p><jats:p>The motivation of this research is to distinguish two classes of \u2135<jats:sub>0<\/jats:sub>-Stable theories:<\/jats:p><jats:p>(1) theories such that all models are almost homogeneous;<\/jats:p><jats:p>(2) theories with 2<jats:sup>\u2135<jats:sub>0<\/jats:sub><\/jats:sup> nonalmost homogeneous models.<\/jats:p><jats:p>The example of theories with Skolem functions [L. 1] (almost homogeneous is then equivalent to homogeneous) seems to indicate a link between these properties and the notion of multidimensionality, and that nonmultidimensional theories are in the first case.<\/jats:p>","DOI":"10.2307\/2273335","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:02:24Z","timestamp":1146952944000},"page":"197-205","source":"Crossref","is-referenced-by-count":9,"title":["Countable models of nonmultidimensional \u2135<sub>0<\/sub>-stable theories"],"prefix":"10.1017","volume":"48","author":[{"given":"Elisabeth","family":"Bouscaren","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Lascar","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200043498_ref006","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1978"},{"key":"S0022481200043498_ref003","volume-title":"Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik","author":"Lascar"},{"key":"S0022481200043498_ref002","first-page":"345","article-title":"Les mod\u00e8les d\u00e9nombrables d'une th\u00e9orie ayant des fonctions de Skolem","volume":"268","author":"Lascar","year":"1981","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200043498_ref004","first-page":"330","volume":"44","author":"Lascar","year":"1979","journal-title":"An introduction to forking"},{"key":"S0022481200043498_ref001","author":"Bouscaren","journal-title":"Countable models of multidimensional \u21350-stable theories"},{"key":"S0022481200043498_ref005","unstructured":"Pillay A. , Weakly homogeneous models (to appear)."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200043498","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T19:36:53Z","timestamp":1558726613000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200043498\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,3]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1983,3]]}},"alternative-id":["S0022481200043498"],"URL":"https:\/\/doi.org\/10.2307\/2273335","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,3]]}}}