{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T05:05:57Z","timestamp":1777439157875,"version":"3.51.4"},"reference-count":14,"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":1197,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a first-order formula <jats:italic>\u03c6(x; y)<\/jats:italic> we introduce and study the characteristic sequence (<jats:italic>P<jats:sub>n<\/jats:sub>: n<\/jats:italic> &lt; <jats:italic>\u03c9<\/jats:italic>) of hypergraphs defined by <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002322_inline1\"\/>. We show that combinatorial and classification theoretic properties of the characteristic sequence reflect classification theoretic properties of <jats:italic>\u03c6<\/jats:italic> and vice versa. The main results are a characterization of NIP and of simplicity in terms of persistence of configurations in the characteristic sequence. Specifically, we show that some tree properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence property manifest themselves in the persistence of complicated configurations under localization.<\/jats:p>","DOI":"10.2178\/jsl\/1286198155","type":"journal-article","created":{"date-parts":[[2010,10,4]],"date-time":"2010-10-04T13:16:13Z","timestamp":1286198173000},"page":"1415-1440","source":"Crossref","is-referenced-by-count":5,"title":["The characteristic sequence of a first-order formula"],"prefix":"10.1017","volume":"75","author":[{"given":"M. E.","family":"Malliaris","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002322_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3002-0"},{"key":"S0022481200002322_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(95)00066-6"},{"key":"S0022481200002322_ref008","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1990"},{"key":"S0022481200002322_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/421004"},{"key":"S0022481200002322_ref004","first-page":"23","volume":"32","author":"Keisler","year":"1967","journal-title":"Ultraproducts which are not saturated"},{"key":"S0022481200002322_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-07-00558-9"},{"key":"S0022481200002322_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2003.11.001"},{"key":"S0022481200002322_ref001","first-page":"817","volume":"64","author":"Buechler","year":"1999","journal-title":"Lascar strong types in some simple theories"},{"key":"S0022481200002322_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.09.008"},{"key":"S0022481200002322_ref011","unstructured":"Shelah , Dependent theories and the generic pair conjecture, arXiv:math.L0\/0702292, 2008."},{"key":"S0022481200002322_ref006","unstructured":"Malliaris , Persistence and regularity in unstable model theory, Ph.D. thesis, University of California, Berkeley, 2009."},{"key":"S0022481200002322_ref013","first-page":"216","volume":"74","author":"Usvyatsov","year":"2009","journal-title":"On generically stable types in dependent theories"},{"key":"S0022481200002322_ref010","first-page":"265","article-title":"Classification theory for elementary classes with the dependence property\u2014a modest beginning","volume":"59","author":"Shelah","year":"2004","journal-title":"Scientiae Mathematicae Japonicae"},{"key":"S0022481200002322_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.02.003"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002322","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T20:36:48Z","timestamp":1556397408000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002322\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["S0022481200002322"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1286198155","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}