{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T17:19:11Z","timestamp":1648660751029},"reference-count":3,"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":18455,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1963,9]]},"abstract":"<jats:p>In [1] Dreben showed that the subclass <jats:italic>K\u2032<\/jats:italic> (described below) of the Suranyi reduction class is recursively solvable by showing that the subclass is <jats:italic>finitely controllable<\/jats:italic>; that is, by showing that any member <jats:italic>S<\/jats:italic> of <jats:italic>K\u2032<\/jats:italic> is satisfiable only if it is finitely satisfiable. Dreben's argument is very complex, but much of the complexity is due to his proving not merely solvability, but the deeper property of finite controllability. In the present note, by exploiting certain features of Dreben's technique, a simpler, direct proof of the solvability of <jats:italic>K\u2032<\/jats:italic> is obtained \u2014 that is, a proof in which the question of satisfiability in a finite domain plays no role.<\/jats:p>","DOI":"10.2307\/2271069","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:21:59Z","timestamp":1146946919000},"page":"237-244","source":"Crossref","is-referenced-by-count":0,"title":["On the solvability of a subclass of the sur\u00e1nyi reduction class"],"prefix":"10.1017","volume":"28","author":[{"given":"Richard","family":"Goldberg","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200117979_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1962-10809-X"},{"key":"S0022481200117979_ref002","first-page":"80","volume-title":"Reduktionstheorie des Entscheidungsproblems im Pr\u00e4dikatenkalk\u00fcl der Ersten Stufe","author":"Sur\u00e1nyi","year":"1959"},{"key":"S0022481200117979_ref001","first-page":"32","article-title":"Solvable Sur\u00e1nyi subclasses: an introduction to the Herbrand theory","volume":"31","author":"Dreben","year":"1962","journal-title":"Annals of the Computation Laboratory of Harvard University"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200117979","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,4]],"date-time":"2019-06-04T19:16:08Z","timestamp":1559675768000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200117979\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1963,9]]},"references-count":3,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1963,9]]}},"alternative-id":["S0022481200117979"],"URL":"https:\/\/doi.org\/10.2307\/2271069","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1963,9]]}}}