{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T23:11:11Z","timestamp":1784848271362,"version":"3.55.0"},"reference-count":10,"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":17025,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1967,8]]},"abstract":"<jats:p><jats:italic>T<jats:sub>0<\/jats:sub><\/jats:italic> will denote G\u00f6del's theory T[3] of functionals of finite type (f.t.) with intuitionistic quantification over each f.t. added. <jats:italic>T<jats:sub>1<\/jats:sub><\/jats:italic> will denote <jats:italic>T<jats:sub>0<\/jats:sub><\/jats:italic> together with definition by bar recursion of type o, the axiom schema of bar induction, and the schema<\/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=\"S0022481200113866_eqnU1\"\/><\/jats:disp-formula><\/jats:p><jats:p>of choice. Precise descriptions of these systems are given below in \u00a74. The main results of this paper are interpretations of <jats:italic>T<jats:sub>0<\/jats:sub><\/jats:italic> in intuitionistic arithmetic <jats:italic>U<jats:sub>0<\/jats:sub><\/jats:italic> and of <jats:italic>T<jats:sub>1<\/jats:sub><\/jats:italic> in intuitionistic analysis is <jats:italic>U<jats:sub>1<\/jats:sub><\/jats:italic>. <jats:italic>U<jats:sub>1<\/jats:sub><\/jats:italic> is <jats:italic>U<jats:sub>0<\/jats:sub><\/jats:italic> with quantification over functionals of type (0,0) and the axiom schemata AC<jats:sub>00<\/jats:sub> and of bar induction.<\/jats:p>","DOI":"10.2307\/2271658","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T16:39:49Z","timestamp":1146933589000},"page":"198-212","source":"Crossref","is-referenced-by-count":385,"title":["Intensional interpretations of functionals of finite type I"],"prefix":"10.1017","volume":"32","author":[{"given":"W. W.","family":"Tait","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200113866_ref010","unstructured":"Tait W. W. , A second order theory of functionals of higher type (to appear)."},{"key":"S0022481200113866_ref007","first-page":"101","volume-title":"Constructivity in mathematics","author":"Kreisel","year":"1959"},{"key":"S0022481200113866_ref005","first-page":"81","volume-title":"Countable functionals, Constructivity in mathematics","author":"Kleene","year":"1959"},{"key":"S0022481200113866_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01447860"},{"key":"S0022481200113866_ref009","first-page":"1","volume-title":"Proceedings of symposia in pure mathematics","author":"Spector","year":"1962"},{"key":"S0022481200113866_ref002","first-page":"34","article-title":"Zur intuitionistischen Arithmetik und Zahlentheorie","author":"G\u00f6del","year":"1931","journal-title":"Ergebnisse eines math. Koll."},{"key":"S0022481200113866_ref008","first-page":"284","volume":"24","author":"Kreisel","year":"1959","journal-title":"Inessential extensions of Heyting's arithmetic by means of functionals of finite type"},{"key":"S0022481200113866_ref006","first-page":"1","article-title":"Recursive functionals and quantifiers of finite type I","volume":"91","author":"Kleene","year":"1959","journal-title":"Transactions of the American Mathematical Society,"},{"key":"S0022481200113866_ref004","doi-asserted-by":"publisher","DOI":"10.4064\/fm-54-1-73-93"},{"key":"S0022481200113866_ref003","doi-asserted-by":"publisher","DOI":"10.1111\/j.1746-8361.1958.tb01464.x"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200113866","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T15:57:28Z","timestamp":1559491048000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200113866\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1967,8]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1967,8]]}},"alternative-id":["S0022481200113866"],"URL":"https:\/\/doi.org\/10.2307\/2271658","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1967,8]]}}}