{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T18:51:10Z","timestamp":1688496670243},"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":10784,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1984,9]]},"abstract":"<jats:p>From the moment choice sequences appear in Brouwer's writings, they do so as elements of a spread. This led Kreisel to take the so-called axiom of spreaddata as the basic axiom in a formal theory of choice sequences (Kreisel [1965, pp. 133\u2013136]). This axiom expresses the idea that to be given a choice sequence means to be given a spread to which the choice sequence belongs. Subsequently, however, it was discovered that there is a formal clash between this axiom and closure of the domain of choice sequences under arbitrary (lawlike) continuous operations (Troelstra [1968]). For this reason, the formal system CS was introduced (Kreisel and Troelstra [1970]), in which spreaddata is replaced by analytic data. In this system CS, the domain of choice sequences is closed under all continuous operations, and therefore it provides a workable basis for intuitionistic analysis. But the problem whether the axiom of spreaddata is compatible with closure of the domain of choice sequences under the continuous operations from a restricted class, which is still rich enough to validate the typical axioms of continuous choice, remained open. It is precisely this problem that we aim to discuss in this paper.<\/jats:p><jats:p>Recall that a <jats:italic>spread<\/jats:italic> is a (lawlike, inhabited) decidable subtree <jats:italic>S<\/jats:italic> of the tree N<jats:sup>&lt; N<\/jats:sup> of all finite sequences, having all branches infinite:<\/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=\"S002248120004305X_eqnU1\" \/><\/jats:disp-formula><\/jats:p>","DOI":"10.2307\/2274144","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:09:38Z","timestamp":1146938978000},"page":"908-916","source":"Crossref","is-referenced-by-count":3,"title":["On choice sequences determined by spreads"],"prefix":"10.1017","volume":"49","author":[{"given":"Gerrit","family":"van der Hoeven","sequence":"first","affiliation":[]},{"given":"Ieke","family":"Moerdijk","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120004305X_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(70)80014-2"},{"key":"S002248120004305X_ref001","first-page":"163","volume-title":"Intuitionism and proof theory","author":"van Dalen","year":"1970"},{"key":"S002248120004305X_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90001-X"},{"key":"S002248120004305X_ref005","unstructured":"van der Hoeven G. F. and Moerdijk I. [1981], Sheaf models for choice sequences, preprint, University of Amsterdam, Amsterdam (to appear in Annals of Pure and Applied Logic )."},{"key":"S002248120004305X_ref003","first-page":"95","volume-title":"Lectures on modern mathematics","volume":"III","author":"Kreisel","year":"1965"},{"key":"S002248120004305X_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71196-0"},{"key":"S002248120004305X_ref002","first-page":"91","volume-title":"Proceedings of the Brouwer centenary conference","author":"Fourman","year":"1982"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120004305X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T15:49:01Z","timestamp":1558626541000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120004305X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1984,9]]}},"alternative-id":["S002248120004305X"],"URL":"https:\/\/doi.org\/10.2307\/2274144","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,9]]}}}