Axiomatic recursion theory and the continuous functionals

Journal of Symbolic Logic 50 (2):442-450 (1985)
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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DOI 10.2307/2274232
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The Continuous Functionals; Computations, Recursions and Degrees.Dag Normann - 1981 - Annals of Mathematical Logic 21 (1):1-26.

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