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

Von Plato, Jan

Indagationes Mathematicae, December 2018, Vol.29(6), pp.1546-1554 [Peer Reviewed Journal]

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  • Title:
    Real numbers and projective spaces: Intuitionistic reasoning with undecidable basic relations
  • Author: Von Plato, Jan
  • Description: 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.
  • Is Part Of: Indagationes Mathematicae, December 2018, Vol.29(6), pp.1546-1554
  • Identifier: ISSN: 0019-3577 ; DOI: 10.1016/j.indag.2017.10.012
  • Subjects: Mathematics
  • Language: English

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