Abstract
The apartness relation was introduced by Brouwer, [1], [2], as a positive analogue of the inequality relation on the continuum. Subsequently Heyting introduced the notion of apartness axiomatically for a treatment of axiomatic geometry and algebra, [7], [8], [9]. In this paper we will take the axiomatic point of view and consider first-order intuitionistic theories of apartness and equality.
The main results below were obtained in 1975 while the first author was a visiting fellow at Wolfson College, Oxford, and the second author a fellow of King’s College, Cambridge
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Bibliograpgy
L. E. J. Brouwer, ‘Begründing der Mengenlehre unabhängig vom Logischen Satz Satz vom ausgeschlossenen Dritten. Zweiter Teil: Theorie der Punktmengen’, Koninklijke Nederlandse Akademie van Wetenschappen, Verhandelingen 127 (1919), pp. 3–33. Also in [3], pp. 191–221.
L. E. J. Brouwer, ‘Intuitionistische Zerlegung mathematischer Grundbegriffe’, Jahresberichte der Deutschen Mathematiker Verein 33 (1923) pp 251-256 Also in [3], pp. 275–280.
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© 1979 D. Reidel Publishing Company, Dordrecht, Holland
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Van Dalen, D., Statman, R. (1979). Equality in the Presence of Apartness. In: Hintikka, J., Niiniluoto, I., Saarinen, E. (eds) Essays on Mathematical and Philosophical Logic. Synthese Library, vol 122. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9825-4_5
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DOI: https://doi.org/10.1007/978-94-009-9825-4_5
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