{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T17:27:06Z","timestamp":1648747626747},"reference-count":12,"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":12520,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An infinitary characterisation of the first-order sentences true in all substructures of a structure <jats:italic>M<\/jats:italic> is used to obtain partial reduction of the decision problem for such sentences to that for Th(<jats:italic>M<\/jats:italic>). For the relational structure \u3008R, \u2264, + \u3009 this gives a decision procedure for the \u2203<jats:italic>x<\/jats:italic>\u2200<jats:italic>y<\/jats:italic>-part of the theory of all substructures, yet we show that the \u2203<jats:italic>x<\/jats:italic><jats:sub>1<\/jats:sub><jats:italic>x<\/jats:italic><jats:sub>2<\/jats:sub>\u2200<jats:italic>y<\/jats:italic>-part, and the entire theory, is \u03a0<jats:sub arrange=\"stack\">1<\/jats:sub><jats:sup arrange=\"stack\">1<\/jats:sup>-complete. The theory of all ordered subsemigroups of \u3008R, \u2264, + \u3009 is also shown \u03a0<jats:sub arrange=\"stack\">1<\/jats:sub><jats:sup arrange=\"stack\">1<\/jats:sup>-complete. Applications in the philosophy of science are mentioned.<\/jats:p>","DOI":"10.2307\/2273297","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:51:21Z","timestamp":1146937881000},"page":"583-598","source":"Crossref","is-referenced-by-count":3,"title":["The theory of all substructures of a structure: Characterisation and decision problems"],"prefix":"10.1017","volume":"44","author":[{"given":"Kenneth L.","family":"Manders","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048465_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/2318447"},{"key":"S0022481200048465_ref002","first-page":"95","volume-title":"Proceedings of the 18th Annual IEEE Symposium, Foundations of Computer Science","year":"1977"},{"key":"S0022481200048465_ref001","first-page":"437","volume-title":"Proceedings of the Tarski Symposium, 1971, Proceedings of Symposia in Pure Mathematics","volume":"25","year":"1974"},{"key":"S0022481200048465_ref013","doi-asserted-by":"crossref","first-page":"171","DOI":"10.4064\/cm-6-1-171-176","volume":"6","year":"1958","journal-title":"Colloquium Mathematicum"},{"key":"S0022481200048465_ref012","first-page":"113","volume":"23","year":"1958","journal-title":"Foundational aspects of theories of measurement"},{"key":"S0022481200048465_ref005","volume-title":"Logical writings","year":"1971"},{"key":"S0022481200048465_ref009","first-page":"607","volume":"36","year":"1971","journal-title":"Negative solution of the decision problem for sentences true in every sub-algebra of \u2329N, +\u232a"},{"key":"S0022481200048465_ref010","first-page":"379","volume":"41","year":"1974","journal-title":"Philosophy of Science"},{"key":"S0022481200048465_ref008","first-page":"249","volume":"11","year":"1970","journal-title":"Soviet Mathematics, Doklady"},{"key":"S0022481200048465_ref007","volume-title":"Necessary conditions for representability","year":"1977"},{"key":"S0022481200048465_ref006","volume-title":"Foundations of measurement","volume":"1","year":"1971"},{"key":"S0022481200048465_ref011","volume-title":"Mathematical logic","year":"1967"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048465","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T16:28:14Z","timestamp":1558888094000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048465\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1979,12]]}},"alternative-id":["S0022481200048465"],"URL":"https:\/\/doi.org\/10.2307\/2273297","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,12]]}}}