{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T16:39:24Z","timestamp":1777912764751,"version":"3.51.4"},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":14072,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1975,9]]},"abstract":"<jats:p>This paper is the third in a series collectively entitled <jats:italic>Formal systems of intuitionistic analysis<\/jats:italic>. The first two are [4] and [5] in the bibliography; in them I attempted to codify Brouwer's mathematical practice. In the present paper, which is independent of [4] and [5], I shall do the same for Bishop's book [1]. There is a widespread current impression, due partly to Bishop himself (see [2]) and partly to Goodman and the author (see [3]) that the theory of G\u00f6del functionals, with quantifiers and choice, is the appropriate formalism for [1]. That this is not so is seen as soon as one really tries to formalize the mathematics of [1] in detail. Even so simple a matter as the definition of the partial function 1\/<jats:italic>x<\/jats:italic> on the nonzero reals is quite a headache, unless one is prepared either to distinguish nonzero reals from reals (a nonzero real being a pair consisting of a real <jats:italic>x<\/jats:italic> and an integer <jats:italic>n<\/jats:italic> with \u2223<jats:italic>x<\/jats:italic>\u2223 &gt; 1\/<jats:italic>n<\/jats:italic>) or, to take the Dialectica interpretation seriously, by adjoining to the G\u00f6del system an axiom saying that every formula is equivalent to its Dialectica interpretation. (See [1, p. 19], [2, pp. 57\u201360] respectively for these two methods.) In more advanced mathematics the complexities become intolerable.<\/jats:p>","DOI":"10.2307\/2272159","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:36:35Z","timestamp":1146951395000},"page":"347-382","source":"Crossref","is-referenced-by-count":122,"title":["Constructive set theory"],"prefix":"10.1017","volume":"40","author":[{"given":"John","family":"Myhill","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200052968_ref006","first-page":"206","volume-title":"Proceedings of the Summer Logic Conference at Cambridge","author":"Myhill","year":"1971"},{"key":"S0022481200052968_ref005","first-page":"151","volume-title":"Intuitionism and proof theory","author":"Myhill","year":"1970"},{"key":"S0022481200052968_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71193-5"},{"key":"S0022481200052968_ref001","volume-title":"Foundations of constructive analysis","author":"Bishop","year":"1967"},{"key":"S0022481200052968_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0073966"},{"key":"S0022481200052968_ref002","first-page":"53","volume-title":"Intuitionism and proof theory","author":"Bishop","year":"1970"},{"key":"S0022481200052968_ref007","unstructured":"Myhill J. and Goodman N. , The axiom of choice and the law of excluded middle (to appear)."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200052968","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T19:21:09Z","timestamp":1559157669000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200052968\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1975,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1975,9]]}},"alternative-id":["S0022481200052968"],"URL":"https:\/\/doi.org\/10.2307\/2272159","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1975,9]]}}}