Programmability in the Set of Real Numbers and Second-Order Recursion

Article type: Research Article

Authors: Skandalis, Kostas

Affiliations: University of Wrocław

Abstract: In this paper we compare two notions of effectiveness in the ordered field of real numbers. The first one is introduced using the notion of program in the sense of algorithmic logic. The second is the recursiveness in Baire space. After an identification of the Baire space with the set of reals using an effective and natural mapping it turns out that these two notions are different. We also study a natural notion of effectiveness extending both these notions.

Keywords: recursive, real function, programmable function, algorithmic logic

DOI: 10.3233/FI-1983-63-404

Journal: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 257-274, 1983