{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,12]],"date-time":"2022-06-12T21:15:25Z","timestamp":1655068525861},"reference-count":12,"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":4210,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:p>We consider only computable languages, and countable structures, with universe a subset of <jats:italic>\u03c9<\/jats:italic>, which we think of as a set of constants. We identify sentences with their G\u00f6del numbers. Thus, for a structure <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009531_inline1\" \/>, the complete (elementary) diagram, <jats:italic>D<jats:sup>c<\/jats:sup><\/jats:italic>(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009531_inline1\" \/>), and the atomic diagram, <jats:italic>D<\/jats:italic>(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009531_inline1\" \/>), are subsets of <jats:italic>\u03c9<\/jats:italic>. We classify formulas as usual. A formula is both \u03a3<jats:sub>0<\/jats:sub> and \u03a0<jats:sub>0<\/jats:sub> if it is open. For <jats:italic>n<\/jats:italic> &gt; 0, a formula, in prenex normal form, is \u03a3<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, or \u03a0<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, if it has <jats:italic>n<\/jats:italic> blocks of like quantifiers, beginning with \u2203, or \u2200. For a formula \u03b8, in prenex normal form, we let neg(\u03b8) denote the dual formula that is logically equivalent to \u00ac\u03b8\u2014if \u03b8 is \u03a3<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, then <jats:italic>neg<\/jats:italic>(\u03b8) is \u03a0<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, and vice versa.<\/jats:p>","DOI":"10.2178\/jsl\/1190150160","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:14:26Z","timestamp":1197555266000},"page":"1227-1247","source":"Crossref","is-referenced-by-count":3,"title":["Sequences of <i>n<\/i>-diagrams"],"prefix":"10.1017","volume":"67","author":[{"given":"Valentina S.","family":"Harizanov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julia F.","family":"Knight","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrei S.","family":"Morozov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009531_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0325-4_19"},{"key":"S0022481200009531_ref009","volume-title":"Logic Colloquium 2001","author":"Knight"},{"key":"S0022481200009531_ref007","first-page":"797","article-title":"Restricted theories of constructive Boolean algebras","volume":"17","author":"Goncharov","year":"1976","journal-title":"Sibirskii Matematicheskii Zhurnal"},{"key":"S0022481200009531_ref006","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1305\/ndjfl\/1039118866","article-title":"An undecidable linear order that is n-decidable for all n","volume":"39","author":"Chisholm","year":"1998","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S0022481200009531_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(96)00026-7"},{"key":"S0022481200009531_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90015-8"},{"key":"S0022481200009531_ref011","first-page":"1447","volume":"66","author":"Knight","year":"2001","journal-title":"Minimality and completions of PA"},{"key":"S0022481200009531_ref005","first-page":"1168","volume":"55","author":"Chisholm","year":"1990","journal-title":"Effective model theory vs. recursive model theory"},{"key":"S0022481200009531_ref004","first-page":"5","volume-title":"Studies in Model Theory","volume":"8","author":"Barwise","year":"1973"},{"key":"S0022481200009531_ref003","volume-title":"Computable Structures and the Hyperarithmetical Hierarchy","author":"Ash","year":"2000"},{"key":"S0022481200009531_ref010","first-page":"1034","volume":"51","author":"Knight","year":"1986","journal-title":"Degrees coded in jumps of orderings"},{"key":"S0022481200009531_ref008","unstructured":"Knight J. F. , Models of arithmetic: quantifiers and complexity, to appear in volume on reverse mathematics ( Simpson S. , editor)."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009531","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T20:45:41Z","timestamp":1557175541000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009531\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,9]]}},"alternative-id":["S0022481200009531"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150160","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}