{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:43Z","timestamp":1761611203784},"reference-count":13,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>There are several open problems in the study of the calculi which result from adding either of Hilbert's \u03f5\u2010 or \u03c4\u2010operators to the first order intuitionistic predicate calculus. This paper provides answers to several of them. In particular, the first complete and sound semantics for these calculi are presented, in both a \u201cquasi\u2010extensional\u201d version which uses choice functions in a straightforward way to interpret the \u03f5\u2010 or \u03c4\u2010terms, and in a form which does not require extensionality assumptions. Unlike the classical case, the addition of either operator to intuitionistic logic is non\u2010conservative. Several interesting consequences of the addition of each operator are proved. Finally, the independence of several other schemes in either calculus are also proved, making use of the semantics supplied earlier in the paper.<\/jats:p>","DOI":"10.1002\/malq.19950410409","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T20:55:17Z","timestamp":1180817717000},"page":"523-546","source":"Crossref","is-referenced-by-count":8,"title":["Intuitionistic \u03f5\u2010 and \u03c4\u2010calculi"],"prefix":"10.1002","volume":"41","author":[{"given":"David","family":"Devidi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19570030104"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01049178"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19930390137"},{"key":"e_1_2_1_5_2","volume-title":"A Course in Mathematical Logic","author":"Bell J. L.","year":"1977"},{"key":"e_1_2_1_6_2","volume-title":"Logic, Bivalence and Denotation","author":"Bencivenga E.","year":"1986"},{"key":"e_1_2_1_7_2","first-page":"644","article-title":"Notes on a semantic analysis of variable binding term operators","volume":"55","author":"Corcoran J.","year":"1971","journal-title":"Logique et Analyse"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19720181202"},{"key":"e_1_2_1_9_2","unstructured":"DeVidi D. Term Forming Operators in First Order Logic. PhD Thesis University of Western Ontario 1994."},{"key":"e_1_2_1_10_2","volume-title":"The Logical Foundations of Mathematics","author":"Hatcher W.","year":"1982"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/2270905"},{"key":"e_1_2_1_12_2","volume-title":"Mathematical Logic and Hilbert's \u03f5\u2010Symbol","author":"Leisenring A. C.","year":"1969"},{"key":"e_1_2_1_13_2","first-page":"97","volume-title":"Selected Papers in Proof Theory","author":"Mints G. E.","year":"1974"},{"key":"e_1_2_1_14_2","volume-title":"The Mathematics of Metamathematics","author":"Rasiowa H.","year":"1968"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410409","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410409","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T16:27:48Z","timestamp":1698251268000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410409"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410409","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}