{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,13]],"date-time":"2023-10-13T04:40:23Z","timestamp":1697172023173},"reference-count":4,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2003,11,26]],"date-time":"2003-11-26T00:00:00Z","timestamp":1069804800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A basic result in intuitionism is \u03a0<jats:sup>0<\/jats:sup><jats:sub>2<\/jats:sub>\u2010conservativity. Take any proof <jats:italic>p<\/jats:italic> in classical arithmetic of some \u03a0<jats:sup>0<\/jats:sup><jats:sub>2<\/jats:sub>\u2010statement (some arithmetical statement \u2200<jats:italic>x<\/jats:italic>.\u2203<jats:italic>y<\/jats:italic>.<jats:italic>P<\/jats:italic>(<jats:italic>x, y<\/jats:italic>), with <jats:italic>P<\/jats:italic> decidable). Then we may effectively turn <jats:italic>p<\/jats:italic> in some intuitionistic proof of the same statement. In a previous paper [1], we generalized this result: any classical proof <jats:italic>p<\/jats:italic> of an arithmetical statement \u2200<jats:italic>x<\/jats:italic>.\u2203<jats:italic>y<\/jats:italic>.<jats:italic>P<\/jats:italic>(<jats:italic>x, y<\/jats:italic>), with <jats:italic>P<\/jats:italic> of degree <jats:italic>k<\/jats:italic>, may be effectively turned into some proof of the same statement, using Excluded Middle only over degree <jats:italic>k<\/jats:italic> formulas. When <jats:italic>k<\/jats:italic> = 0, we get the original conservativity result as particular case. This result was a by\u2010product of a semantical construction. J. Avigad of Carnegie Mellon University, found a short, direct syntactical derivation of the same result, using H. Friedman's <jats:italic>A<\/jats:italic>\u2010translation. His proof is included here with his permission. (\u00a9 2003 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310074","type":"journal-article","created":{"date-parts":[[2004,1,16]],"date-time":"2004-01-16T15:51:49Z","timestamp":1074268309000},"page":"41-46","source":"Crossref","is-referenced-by-count":5,"title":["A generalization of a conservativity theorem for classical versus intuitionistic arithmetic"],"prefix":"10.1002","volume":"50","author":[{"given":"Stefano","family":"Berardi","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2003,11,26]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"S.Berardi Classical Logic as Limit II. Technical Report University of Torino June 20027). Available under: http:\/\/www.di.unito.it\/\u223cstefano\/Berardi\u2010ClassicalLogicAsLimit\u2010II.rtf.7)For the proof of generalized conservativity see page 48 Faithfulness Theorem point 2."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"H.Friedman Classically and intuitionistically provable recursive functions. In: Higher Set Theory (D. S. Scott and G. H. M\u00fcller eds.) Lecture Notes in Mathematics 699 pp. 21\u201328 (Springer\u2010Verlag Berlin 1978).","DOI":"10.1007\/BFb0103100"},{"key":"e_1_2_1_4_2","unstructured":"K.G\u00f6del On intuitionistic arithmetic and number theory. In: The Undecidable (M. Davis ed.) pp. 75\u201381 (Raven Press Hewlett 1965)."},{"key":"e_1_2_1_5_2","unstructured":"C.Murphy Extracting constructive content from classical proofs. Ph. D. Thesis Cornell University August 1990."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310074","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310074","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310074","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T08:59:34Z","timestamp":1697101174000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310074"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,11,26]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1002\/malq.200310074"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310074","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,11,26]]}}}