Real numbers and projective spaces : Intuitionistic reasoning with undecidable basic relations

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dc.contributor University of Helsinki, Gödeliana en
dc.contributor.author von Plato, Jan
dc.date.accessioned 2020-06-28T00:16:36Z
dc.date.available 2021-06-16T02:47:13Z
dc.date.issued 2018-12
dc.identifier.citation von Plato , J 2018 , ' Real numbers and projective spaces : Intuitionistic reasoning with undecidable basic relations ' , Indagationes Mathematicae , vol. 29 , no. 6 , pp. 1546-1554 . https://doi.org/10.1016/j.indag.2017.10.012 en
dc.identifier.issn 0019-3577
dc.identifier.other PURE: 108395426
dc.identifier.other PURE UUID: 81f15607-8887-4a7f-b217-2409157be8b8
dc.identifier.other RIS: urn:EE6D7C441773E4721038D611329900B6
dc.identifier.other Scopus: 85049877130
dc.identifier.other WOS: 000449141600007
dc.identifier.uri http://hdl.handle.net/10138/317010
dc.description.abstract Brouwer introduced in 1924 the notion of an apartness relation for real numbers, with the idea that whenever it holds, a finite computation verifies it in contrast to equality. The idea was followed in Heyting's axiomatization of intuitionistic projective geometry. Brouwer in turn worked out an intuitionistic theory of "virtual order." It is shown that Brouwer's proof of the equivalence of virtual and maximal order goes only in one direction, and that Heyting's axiomatization needs to be made a bit stronger. (C) 2018 Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). en
dc.format.extent 9
dc.language.iso eng
dc.relation.ispartof Indagationes Mathematicae
dc.rights en
dc.subject 111 Mathematics en
dc.subject geometry en
dc.title Real numbers and projective spaces : Intuitionistic reasoning with undecidable basic relations en
dc.type Article
dc.description.version Peer reviewed
dc.identifier.doi https://doi.org/10.1016/j.indag.2017.10.012
dc.type.uri info:eu-repo/semantics/other
dc.type.uri info:eu-repo/semantics/acceptedVersion
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