{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T09:12:32Z","timestamp":1721034752067},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":19734,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1960,3]]},"abstract":"In a previous paper [1] it was proved, among other results, that a closed disjunction of intuitionistic elementary number theory N<\/jats:bold> can be proved if and only if at least one of its disjunctands is provable and that a closed formula of the type (Ex)B(x)<\/jats:italic> is provable in N<\/jats:bold> if and only if B(n)<\/jats:italic> is provable for some numeral n<\/jats:italic>. The method of proof was to show that, as far as closed formulas are concerned, N<\/jats:bold> is equivalent to a calculus N1<\/jats:sub><\/jats:bold> for which the result is immediate. The main step in the proof consisted in showing that the set of provable formulas of N1<\/jats:sub><\/jats:bold> is closed under modus ponens. This was done by obtaining a subset of the set which is closed under modus ponens and contains all members of the original set, with which it is therefore identical.<\/jats:p>","DOI":"10.2307\/2964334","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:07:48Z","timestamp":1146946068000},"page":"27-32","source":"Crossref","is-referenced-by-count":88,"title":["Concerning formulas of the types A\u2192B<\/i> \u03bd C,A \u2192(Ex)B(x)<\/i> in intuitionistic formal systems"],"prefix":"10.1017","volume":"25","author":[{"given":"Ronald","family":"Harrop","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200122662_ref002","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"},{"key":"S0022481200122662_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01360048"},{"key":"S0022481200122662_ref003","first-page":"456","article-title":"The non-derivability of \u2138 (x)A(x) \u2192 (Ex)A(x), A primitive recursive, in intuitionistic formal systems (abstract)","volume":"23","author":"Kreisel","year":"1958","journal-title":"this Journal"},{"key":"S0022481200122662_ref004","first-page":"101","volume-title":"Constructivity in mathematics","author":"Kreisel","year":"1958"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200122662","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T19:42:21Z","timestamp":1559763741000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200122662\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1960,3]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1960,3]]}},"alternative-id":["S0022481200122662"],"URL":"https:\/\/doi.org\/10.2307\/2964334","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1960,3]]}}}