{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T06:17:47Z","timestamp":1791181067098,"version":"4.1.0"},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":16301,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb.\n                        log."],"published-print":{"date-parts":[[1969,7,25]]},"abstract":"<jats:p>Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200094391_inline1\"\/> be a\n                        relational system whereby <jats:italic>D<\/jats:italic> is a nonempty set and\n                              <jats:italic>P<jats:sub>1<\/jats:sub><\/jats:italic> is an\n                        <jats:italic>m<jats:sub>1<\/jats:sub><\/jats:italic>-ary relation on <jats:italic>D<\/jats:italic>. With\n                           <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200094391_inline2\"\/> we associate the (weak) monadic second-order theory\n                           <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200094391_inline3\"\/> consisting of the first-order predicate calculus\n                        with individual variables ranging over <jats:italic>D<\/jats:italic>; monadic predicate\n                        variables ranging over (finite) subsets of <jats:italic>D<\/jats:italic>; monadic\n                        predicate quantifiers; and constants corresponding to <jats:italic>P<jats:sub>1<\/jats:sub>,\n                              P<jats:sub>2<\/jats:sub><\/jats:italic>, \u2026. We will often use <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200094391_inline4\"\/> ambiguously to mean also the set of true sentences\n                        of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200094391_inline5\"\/>.<\/jats:p>","DOI":"10.2307\/2271090","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:53:51Z","timestamp":1146948831000},"page":"166-170","source":"Crossref","is-referenced-by-count":46,"title":["Definability in the monadic second-order theory of\n                           successor"],"prefix":"10.1017","volume":"34","author":[{"given":"J.","family":"Richard Buchi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lawrence H.","family":"Landweber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200094391_ref001","volume-title":"Proceedings of the international congress on logic, methodology and the philosophy of science","author":"B\u00fcchi","year":"1962"},{"key":"S0022481200094391_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1955-09896-3"},{"key":"S0022481200094391_ref005","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"},{"key":"S0022481200094391_ref009","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200094391_ref004","first-page":"169","article-title":"Decidability and undecidability of extensions of second (first) order theories of (generalized) successor","volume":"31","author":"Elgot","year":"1966","journal-title":"this Journal"},{"key":"S0022481200094391_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(66)80013-X"},{"key":"S0022481200094391_ref003","first-page":"85","volume-title":"Advances in game theory","author":"Davis","year":"1964"},{"key":"S0022481200094391_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1958-0093479-4"},{"key":"S0022481200094391_ref002","volume-title":"Solving sequential conditions by finite state operators","author":"B\u00fcchi"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200094391","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T06:34:55Z","timestamp":1679466895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200094391\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1969,7,25]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1969,7,25]]}},"alternative-id":["S0022481200094391"],"URL":"https:\/\/doi.org\/10.2307\/2271090","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1969,7,25]]}}}