{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T22:52:44Z","timestamp":1648507964298},"reference-count":2,"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":20373,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1958,6]]},"abstract":"<jats:p>In attempting to reconstruct Rose's proof of Lemma 3.2 of [1], the present authors found what is apparently a different and simpler method, which moreover leads to a far stronger conclusion.<\/jats:p><jats:p>We are operating in the Heyting prepositional calculus as formulated on p. 3 of [1] or on pp. 82 and 101 of [2], and shall make use of relevant theorems on pp. 90, 113\u2013119 of [2]. We shall use a, b, c, w, x, y, z as propositional variables.<\/jats:p><jats:p>We say that a conjunction is simple if each factor has one of the forms: (i) a, (ii) \u00aca, (iii) a\u2283b, (iv) a\u2283(b\u2228c), (v) (a&amp;b)\u2283c, (vi) (a\u2283b)\u2283c.<\/jats:p>","DOI":"10.2307\/2964393","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T19:56:53Z","timestamp":1146945413000},"page":"137-138","source":"Crossref","is-referenced-by-count":1,"title":["Generalization of a lemma of G. F. Rose"],"prefix":"10.1017","volume":"23","author":[{"given":"I. L.","family":"G\u00e1l","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. B.","family":"Rosser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"Scott","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200058473_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1953-0055952-4"},{"key":"S0022481200058473_ref002","first-page":"550","volume-title":"Introduction to Metamathematics","author":"Kleene","year":"1952"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200058473","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T20:42:02Z","timestamp":1559767322000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200058473\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1958,6]]},"references-count":2,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1958,6]]}},"alternative-id":["S0022481200058473"],"URL":"https:\/\/doi.org\/10.2307\/2964393","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1958,6]]}}}