Axiomatic Recursion Theory and the Continuous Functionals
Simon Thompson
Source: J. Symbolic Logic Volume 50, Issue 2 (1985), 442-450.
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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Mathematical Reviews number (MathSciNet):
MR793124
Zentralblatt MATH identifier:
0589.03031
