{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T02:36:49Z","timestamp":1697942209752},"reference-count":7,"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":23203,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1950,9]]},"abstract":"<jats:p>It has been proved by Pepis that any formula of the first-order predicate calculus is equivalent (in respect of being satisfiable) to another with a prefix of the form<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200103123_equ1\" \/><\/jats:disp-formula><\/jats:p><jats:p>containing a single existential quantifier. In this paper, we shall improve this theorem in the like manner as the Ackermann and the G\u00f6del reduction theorems have been improved in the preceding papers of the same main title. More explicitly, we shall prove the<\/jats:p><jats:p>Theorem 1. <jats:italic>To any given first-order formula it is possible to construct an equivalent one with a prefix of the form<\/jats:italic> (1) <jats:italic>and a matrix containing no other predicate variable than a single binary one<\/jats:italic>.<\/jats:p><jats:p>An analogous theorem, but producing a prefix of the form<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200103123_equ2\" \/><\/jats:disp-formula><\/jats:p><jats:p>has been proved in the meantime by Sur\u00e1nyi; some modifications in the proof, suggested by Kalm\u00e1r, led to the above form.<\/jats:p>","DOI":"10.2307\/2266781","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T19:12:14Z","timestamp":1146942734000},"page":"161-173","source":"Crossref","is-referenced-by-count":6,"title":["On the reduction of the decision problem. Third paper. Pepis prefix, a single binary predicate"],"prefix":"10.1017","volume":"15","author":[{"given":"L\u00e1szl\u00f3","family":"Kalm\u00e1r","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00e1nos","family":"Sur\u00e1nyi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200103123_ref007","first-page":"1","volume-title":"Videnskapsselskapets skrifter, Kristiania","author":"Skolem","year":"1920"},{"key":"S0022481200103123_ref005","first-page":"51","article-title":"Zur Reduktion des Entscheidungsproblems des logischen Funktionenkalk\u00fcls","volume":"50","year":"1943","journal-title":"Matematikai \u00e9s fizikai lapok"},{"key":"S0022481200103123_ref001","first-page":"III","volume":"18","year":"1945","journal-title":"Annales de la Soci\u00e9t\u00e9 Polonaise de Math\u00e9matique"},{"key":"S0022481200103123_ref003","doi-asserted-by":"publisher","DOI":"10.4064\/fm-30-1-257-348"},{"key":"S0022481200103123_ref006","first-page":"1","volume-title":"Skrifter utgitt av det Norske Videnskaps-Akademi i Oslo","author":"Skolem","year":"1929"},{"key":"S0022481200103123_ref004","first-page":"1","volume":"4","author":"Kalm\u00e1r","year":"1939","journal-title":"On the reduction of the decision problem, first paper, Ackermann prefix, a single binary predicate"},{"key":"S0022481200103123_ref002","first-page":"61","volume":"3","author":"Pepis","year":"1938","journal-title":"Ein Verfahren der mathematischen Logik"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200103123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T10:14:17Z","timestamp":1559988857000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200103123\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1950,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1950,9]]}},"alternative-id":["S0022481200103123"],"URL":"https:\/\/doi.org\/10.2307\/2266781","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1950,9]]}}}