A blend of methods of recursion theory and topology

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Annals of Pure and Applied Logic 124 (1-3):141-178 (2003)
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Abstract

This paper is a culmination of our new foundations for recursive analysis through recursive topology as reported in Kalantari and Welch 125; 98 87). While in those papers we developed groundwork for an approach to point free analysis and applied recursion theory, in this paper we blend techniques of recursion theory with those of topology to establish new findings. We present several new techniques different from existing ones which yield interesting results. Incidental to our work is a unifying explanation of various schools of study for recursive analysis

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10.1016/s0168-0072(03)00054-x

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Citations of this work

Closed choice and a uniform low basis theorem.Vasco Brattka, Matthew de Brecht & Arno Pauly - 2012 - Annals of Pure and Applied Logic 163 (8):986-1008.
Demuth’s path to randomness.Antonín Kučera, André Nies & Christopher P. Porter - 2015 - Bulletin of Symbolic Logic 21 (3):270-305.
On Turing degrees of points in computable topology.Iraj Kalantari & Larry Welch - 2008 - Mathematical Logic Quarterly 54 (5):470-482.

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References found in this work

On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.

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