A Constructive Morse Theory of Sets

Douglas S. Bridges
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Douglas S. Bridges: University of Buckingham

A chapter in Mathematical Logic and Its Applications, 1987, pp 61-79 from Springer

Abstract: Abstract In this paper I shall outline a foundational system for constructive mathematics analogous to that given in [11] for classical mathematics. By ‘constructive mathematics’ I shall mean mathematics as understood by Errett Bishop and his followers [2, 3], the mathematics of which the primary concern … is number, and this means the positive integers … Everything attaches itself to number, and every mathematical statement ultimately expresses the fact that if we perform certain computations within the set of positive integers, we shall get certain results. [2, pp. 2–3] In other words, mathematics as we understand it is characterised by numerical content and computational meaning.

Date: 1987
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DOI: 10.1007/978-1-4613-0897-3_5

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