{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,16]],"date-time":"2023-09-16T09:11:22Z","timestamp":1694855482526},"reference-count":8,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2018,10,18]],"date-time":"2018-10-18T00:00:00Z","timestamp":1539820800000},"content-version":"am","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"},{"start":{"date-parts":[[2018,10,18]],"date-time":"2018-10-18T00:00:00Z","timestamp":1539820800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1650069"],"award-info":[{"award-number":["1650069"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,11]]},"abstract":"Abstract<\/jats:title>Working in (Intuitionistic analysis) we prove a strong, constructive connectedness property of the continuum: for any non\u2010empty sets, A<\/jats:italic> and B<\/jats:italic>, if then is non\u2010empty. It is well known that the intuitionistic continuum is indecomposable<\/jats:italic>: if and then or , but this property is essentially negative\u2014equivalent to if A<\/jats:italic>, B<\/jats:italic> are non\u2010empty and then . Our connectedness property is positive; so, given , , and a witness to , to prove our theorem we must construct a real number . We can construct the needed real number using only Bishop's constructive mathematics () and a weak form of Brouwer's continuity principle (and the choice principles that come from the Brouwer\u2010Heyting\u2010Kolmogorov interpretation of quantifiers in constructive type theory). We also replace indecomposability by connectedness in some results of van Dalen that use additional intuitionistic axioms.<\/jats:p>","DOI":"10.1002\/malq.201700057","type":"journal-article","created":{"date-parts":[[2018,10,28]],"date-time":"2018-10-28T21:00:41Z","timestamp":1540760441000},"page":"387-394","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Connectedness of the continuum in intuitionistic mathematics"],"prefix":"10.1002","volume":"64","author":[{"given":"Mark","family":"Bickford","sequence":"first","affiliation":[{"name":"Department of Computer Science Cornell University Bill and Melinda Gates Hall, 107 Hoy Rd Ithaca NY 14853 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,10,18]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61667-9"},{"key":"e_1_2_9_3_1","first-page":"153","volume-title":"13th International Conference on Typed Lambda Calculi and Applications","author":"Escard\u00f3 M. H.","year":"2015"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/jzn006"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/jzp002"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700018383"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2854065.2854077"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275631"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)70750-X"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201700057","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201700057","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.201700057","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/api.wiley.com\/onlinelibrary\/chorus\/v1\/articles\/10.1002%2Fmalq.201700057","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201700057","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201700057","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T20:46:55Z","timestamp":1694810815000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201700057"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,18]]},"references-count":8,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["10.1002\/malq.201700057"],"URL":"https:\/\/doi.org\/10.1002\/malq.201700057","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,18]]},"assertion":[{"value":"2017-09-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-02-22","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-10-18","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}