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Axiomatic Recursion Theory and the Continuous Functionals
The Journal of Symbolic Logic
Vol. 50, No. 2 (Jun., 1985), pp. 442-450
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2274232
Page Count: 9
You can always find the topics here!Topics: Recursion, Recursion theory, Mathematical logic, Inductive definitions, Recursive functions, Mathematical constants, Axioms, Mathematical monotonicity, Perceptron convergence procedure, Property lines
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We define, in the spirit of Fenstad , 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  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.
The Journal of Symbolic Logic © 1985 Association for Symbolic Logic