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Axiomatic Recursion Theory and the Continuous Functionals

Simon Thompson
The Journal of Symbolic Logic
Vol. 50, No. 2 (Jun., 1985), pp. 442-450
DOI: 10.2307/2274232
Stable URL: http://www.jstor.org/stable/2274232
Page Count: 9
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Axiomatic Recursion Theory and the Continuous Functionals
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Abstract

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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