Bulletin of Symbolic Logic

Alan Turing and the foundations of computable analysis

Guido Gherardi

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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.

Article information

Source
Bull. Symbolic Logic Volume 17, Issue 3 (2011), 394-430.

Dates
First available in Project Euclid: 6 July 2011

Permanent link to this document
http://projecteuclid.org/euclid.bsl/1309952319

Digital Object Identifier
doi:10.2178/bsl/1309952319

Zentralblatt MATH identifier
05956504

Mathematical Reviews number (MathSciNet)
MR2856079

Citation

Gherardi, Guido. Alan Turing and the foundations of computable analysis. Bulletin of Symbolic Logic 17 (2011), no. 3, 394--430. doi:10.2178/bsl/1309952319. http://projecteuclid.org/euclid.bsl/1309952319.


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