Journal of Symbolic Logic

Axiomatic Recursion Theory and the Continuous Functionals

Simon Thompson

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We define, in the spirit of Fenstad [2], a higher type computation theory, and show that countable recursion over the continuous functionals forms such a theory. We also discuss Hyland's proposal from [4] for a scheme with which to supplement S1-S9, and show that this augmented set of schemes fails to generate countable recursion. We make another proposal to which the methods of this section do not apply.

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J. Symbolic Logic, Volume 50, Issue 2 (1985), 442-450.

First available in Project Euclid: 6 July 2007

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Thompson, Simon. Axiomatic Recursion Theory and the Continuous Functionals. J. Symbolic Logic 50 (1985), no. 2, 442--450.

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