{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T18:59:55Z","timestamp":1766084395041},"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":10784,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1984,9]]},"abstract":"<jats:p>In classical prepositional calculus for each proposition <jats:italic>A(p)<\/jats:italic> the following holds: \u22a2<jats:italic>A(p)<\/jats:italic> \u2194 <jats:italic>A<jats:sup>3<\/jats:sup>(p)<\/jats:italic>. In this paper we consider what remains of this in the intuitionistic case. It turns out that for each proposition <jats:italic>A(p)<\/jats:italic> the following holds: there is an <jats:italic>n<\/jats:italic> \u2208 N such that<\/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=\"S0022481200043036_eqnU1\" \/><\/jats:disp-formula><\/jats:p><jats:p>As a byproduct of the proof we give some theorems which may be useful elsewhere in propositional calculus.<\/jats:p>","DOI":"10.2307\/2274142","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:09:38Z","timestamp":1146953378000},"page":"892-899","source":"Crossref","is-referenced-by-count":14,"title":["On the period of sequences (<i>A<sup>n<\/sup>(p)<\/i>) in intuitionistic propositional calculus"],"prefix":"10.1017","volume":"49","author":[{"given":"Wim","family":"Ruitenburg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200043036_ref002","unstructured":"Smory\u0144ski C. , Applications of the Kripke models, in [3, pp. 324\u2013391]."},{"key":"S0022481200043036_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066739"},{"key":"S0022481200043036_ref001","first-page":"327","volume":"25","author":"Nishimura","year":"1960","journal-title":"On formulas in one variable in intuitionistic propositional calculus"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200043036","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T19:49:21Z","timestamp":1558640961000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200043036\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,9]]},"references-count":3,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1984,9]]}},"alternative-id":["S0022481200043036"],"URL":"https:\/\/doi.org\/10.2307\/2274142","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,9]]}}}