Alan Turing and the foundations of computable analysis

Bulletin of Symbolic Logic 17 (3):394-430 (2011)

Abstract

We investigate Turing's contributions to computability theory for real numbers and real functions presented in [22, 24, 26]. In particular, it is shown how two fundamental approaches to computable analysis, the so-called ‘Type-2 Theory of Effectivity' (TTE) and the ‘realRAM machine' model, have their foundations in Turing's work, in spite of the two incompatible notions of computability they involve. It is also shown, by contrast, how the modern conceptual tools provided by these two paradigms allow a systematic interpretation of Turing's pioneering work in the subject

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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.
Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Computability and Λ-Definability.A. M. Turing - 1937 - Journal of Symbolic Logic 2 (4):153-163.
Recursive Unsolvability of a Problem of Thue.Emil L. Post - 1947 - Journal of Symbolic Logic 12 (1):1-11.

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Citations of this work

The Representational Foundations of Computation.Michael Rescorla - 2015 - Philosophia Mathematica 23 (3):338-366.
Turing Meets Schanuel.Angus Macintyre - 2016 - Annals of Pure and Applied Logic 167 (10):901-938.

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