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Heyting and Intuitionistic Geometry

In: Mathematical Logic

Author

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  • D. van Dalen

    (State University of Utrecht, Mathematical Institute)

Abstract

It may seem strange that the second fully committed intuitionist in mathematics entered his career with a treatise on axiomatic geometry, for axiomatics did have a formalist flavour and one cannot suspect Brouwer, Heyting’s teacher, of leanings in that specific direction. There are a number of possible explanations for the choice of this particular topic — which, by the way, had been suggested by Brouwer. One of them is Brouwer’s own interest in the foundations of geometry in the Pasch-Hilbert-style; his Ph.D.Thesis contained a good deal of geometry and he regularly lectured on the foundations of geometry. His inaugural address as a “privaat docent” bore the title “The nature of geometry”. Hence it is not all that surprising that Heyting choose the intuitionistic foundations as a topic for his Ph.D.thesis.

Suggested Citation

  • D. van Dalen, 1990. "Heyting and Intuitionistic Geometry," Springer Books, in: Petio Petrov Petkov (ed.), Mathematical Logic, pages 19-27, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0609-2_2
    DOI: 10.1007/978-1-4613-0609-2_2
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