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Alan Turing and the Foundations of Computable Analysis

Published online by Cambridge University Press:  15 January 2014

Guido Gherardi
Guido Gherardi*
Affiliation:
Dipartimento Di Filosofia, Universitá Du Bologna, Via Zamboni 38, 40126 Bologna, ItalyE-mail: guido.gherardi@unibo.it
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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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 17 , Issue 3 , September 2011 , pp. 394 - 430
Copyright
Copyright © Association for Symbolic Logic 2011

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