{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T13:59:54Z","timestamp":1773237594409,"version":"3.50.1"},"reference-count":7,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2008,5,6]],"date-time":"2008-05-06T00:00:00Z","timestamp":1210032000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2008,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Is it possible to give an abstract characterisation of constructive real numbers? A condition should be that all axioms are valid for Dedekind reals in any topos, or for constructive reals in Bishop mathematics. We present here a possible first\u2010order axiomatisation of real numbers, which becomes complete if one adds the law of excluded middle. As an application of the forcing relation defined in [3, 2], we give a proof that the formula which specifies the maximum function is not provable in this theory. (\u00a9 2008 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710039","type":"journal-article","created":{"date-parts":[[2008,5,6]],"date-time":"2008-05-06T03:51:58Z","timestamp":1210045918000},"page":"224-228","source":"Crossref","is-referenced-by-count":1,"title":["A note on the axiomatisation of real numbers"],"prefix":"10.1002","volume":"54","author":[{"given":"Thierry","family":"Coquand","sequence":"first","affiliation":[]},{"given":"L. Henri","family":"Lombardi","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2008,5,6]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"J.Bochnak M.Coste andM. F.Roy G\u00e9om\u00e9trie Alg\u00e9brique R\u00e9elle (Springer\u2010Verlag 1987)."},{"key":"e_1_2_1_3_2","unstructured":"T.Coquand A completeness proof for geometrical logic. In: Logic Methodology and Philosophy of Sciences (P. H\u00e1jek L. Valdes\u2010Villanueva and D. Westerstahl eds.) pp. 79\u201390 (College Publications 2005)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(01)00026-4"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(86)90068-X"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(76)90002-5"},{"key":"e_1_2_1_7_2","unstructured":"L. H.Lombardi Constructive real algebra. Talk given at the MAP meeting Leiden 2007."},{"key":"e_1_2_1_8_2","unstructured":"A.Troelstra andD.van Dalen Constructivism in Mathematics. An Introduction. Volume II (North\u2010Holland 1988)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710039","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200710039","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T05:25:15Z","timestamp":1699939515000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200710039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5,6]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["10.1002\/malq.200710039"],"URL":"https:\/\/doi.org\/10.1002\/malq.200710039","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5,6]]}}}