{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:52:20Z","timestamp":1772448740355,"version":"3.50.1"},"reference-count":20,"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":1896,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a countable structure <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200126507_inline1\"\/>, the <jats:italic>spectrum<\/jats:italic> is the set of Turing degrees of isomorphic copies of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200126507_inline1\"\/>. For a complete elementary first order theory <jats:italic>T<\/jats:italic>, the <jats:italic>spectrum<\/jats:italic> is the set of Turing degrees of models of <jats:italic>T<\/jats:italic>. We answer a question from [1] by showing that there is an atomic theory <jats:italic>T<\/jats:italic> whose spectrum does not match the spectrum of any structure.<\/jats:p>","DOI":"10.2178\/jsl.7804100","type":"journal-article","created":{"date-parts":[[2014,1,5]],"date-time":"2014-01-05T20:33:25Z","timestamp":1388954005000},"page":"1189-1198","source":"Crossref","is-referenced-by-count":2,"title":["Spectra of Atomic Theories"],"prefix":"10.1017","volume":"78","author":[{"given":"Uri","family":"Andrews","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julia F.","family":"Knight","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200126507_ref011","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565670.011"},{"key":"S0022481200126507_ref016","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/005\/0141595"},{"key":"S0022481200126507_ref004","unstructured":"Diamondstone D. , Greenberg N. , and Turetsky D. , Inherent enumerability of strong jump-traceability, pre-print."},{"key":"S0022481200126507_ref015","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1984-0732105-5"},{"key":"S0022481200126507_ref009","first-page":"106","volume":"59","author":"Knight","year":"1994","journal-title":"Nonarithmetical \u21350-categorical theories with recursive models"},{"key":"S0022481200126507_ref017","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-98-04307-X"},{"key":"S0022481200126507_ref007","first-page":"68","article-title":"Constructive Abelian p-groups","volume":"2","author":"Khisamiev","year":"1992","journal-title":"Siberian Advances in Mathematics"},{"key":"S0022481200126507_ref002","volume-title":"Computable structures and the hyperarithmetical hierarchy","author":"Ash","year":"2000"},{"key":"S0022481200126507_ref001","doi-asserted-by":"crossref","unstructured":"Andrews U. and Miller J. S. , Spectra of theories and structures, Proceedings of the American Mathematical Society , to appear.","DOI":"10.1090\/S0002-9939-2014-12283-0"},{"key":"S0022481200126507_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80008-6"},{"key":"S0022481200126507_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200910001"},{"key":"S0022481200126507_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-03-06951-X"},{"key":"S0022481200126507_ref006","unstructured":"Greenberg N. , Montalb\u00e1n A. , and Slaman T. 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M. , personal correspondence, 1991."},{"key":"S0022481200126507_ref020","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-98-04314-7"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200126507","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T02:20:17Z","timestamp":1555986017000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200126507\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["S0022481200126507"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7804100","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}