{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T15:39:41Z","timestamp":1767195581033,"version":"build-2238731810"},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8228,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1991,9]]},"abstract":"<jats:p>\n                    By a variety, we mean a class of structures in some language\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200024014_inline1.png\"\/>\n                    containing only function symbols which is equationally defined or equivalently is closed under homomorphisms, submodels and products.\n                  <\/jats:p>\n                  <jats:p>\n                    If\n                    <jats:italic>K<\/jats:italic>\n                    is a class of\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200024014_inline1.png\"\/>\n                    -structures then\n                    <jats:italic>I<\/jats:italic>\n                    (\n                    <jats:italic>K<\/jats:italic>\n                    , \u03bb) denotes the number of nonisomorphic models in\n                    <jats:italic>K<\/jats:italic>\n                    of cardinality \u03bb. When we say that\n                    <jats:italic>K<\/jats:italic>\n                    has few models, we mean that\n                    <jats:italic>I<\/jats:italic>\n                    (\n                    <jats:italic>K<\/jats:italic>\n                    ,\u03bb) &lt; 2\n                    <jats:sup>\u03bb<\/jats:sup>\n                    for some \u03bb &gt; \u2223\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200024014_inline1.png\"\/>\n                    \u2223. If\n                    <jats:italic>I<\/jats:italic>\n                    (\n                    <jats:italic>K<\/jats:italic>\n                    ,\u03bb) = 2\n                    <jats:sup>\u03bb<\/jats:sup>\n                    for all \u03bb &gt; \u2223\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200024014_inline1.png\"\/>\n                    \u2223, then we say\n                    <jats:italic>K<\/jats:italic>\n                    has many models. In [9] and [10], Shelah has shown that for an elementary class\n                    <jats:italic>K<\/jats:italic>\n                    , having few models is a strong structural condition.\n                  <\/jats:p>","DOI":"10.2178\/jsl\/1183743732","type":"journal-article","created":{"date-parts":[[2009,8,4]],"date-time":"2009-08-04T16:52:04Z","timestamp":1249404724000},"page":"832-852","source":"Crossref","is-referenced-by-count":11,"title":["A structure theorem for strongly abelian varieties with few models"],"prefix":"10.1017","volume":"56","author":[{"given":"Bradd","family":"Hart","sequence":"first","affiliation":[]},{"given":"Matthew","family":"Valeriote","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200024014_ref009","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1978"},{"key":"S0022481200024014_ref007","first-page":"278","article-title":"Models of superstable Horn theories","volume":"24","author":"Saffe","year":"1985","journal-title":"Algebra i Logika"},{"key":"S0022481200024014_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07330-8"},{"key":"S0022481200024014_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600562"},{"key":"S0022481200024014_ref005","first-page":"789","article-title":"Spectra of varieties","volume":"306","author":"Palyutin","year":"1989","journal-title":"Doklady AkademiiNauk SSSR"},{"key":"S0022481200024014_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4552-0"},{"key":"S0022481200024014_ref006","first-page":"1298","article-title":"Spectra of Horn classes","volume":"290","author":"Palyutin","year":"1986","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S0022481200024014_ref003","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870822"},{"key":"S0022481200024014_ref011","unstructured":"Valeriote M. , On decidable locally finite varieties, Ph.D. thesis, University of California, Berkeley, California, 1986."},{"key":"S0022481200024014_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02483731"},{"key":"S0022481200024014_ref010","unstructured":"Shelah S. , The spectrum problem. 4: The main gap for countable theories, to be included in the forthcoming revised edition of [9]."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200024014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T06:34:37Z","timestamp":1679466877000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200024014\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,9]]},"references-count":11,"aliases":["10.2307\/2275053"],"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,9]]}},"alternative-id":["S0022481200024014"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1183743732","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,9]]}}}