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

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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

Title: Real numbers and projective spaces : Intuitionistic reasoning with undecidable basic relations
Author: von Plato, Jan
Contributor: University of Helsinki, Gödeliana
Date: 2018-12
Language: eng
Number of pages: 9
Belongs to series: Indagationes Mathematicae
ISSN: 0019-3577
URI: http://hdl.handle.net/10138/317010
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).
Subject: 111 Mathematics
geometry
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