Recursive functionals and quantifiers of finite types revisited. V
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- by S. C. Kleene PDF
- Trans. Amer. Math. Soc. 325 (1991), 593-630 Request permission
Abstract:
This is the last in a sequence of papers that redoes the theory of recursion in finite types. A key feature of the theory is that a computation can succeed (or finish) even if some of its subcomputations do not, if these turn out to be irrelevant to the total computation. I give a detailed description of computations involving oracles for type $3$ functionals. The computation may be viewed formally as a transfinite sequence of symbolic expressions, but I also describe a semantics in which each expression is given a concrete realization.References
- S. C. Kleene, Recursive functionals and quantifiers of finite types revisited. I, Generalized recursion theory, II (Proc. Second Sympos., Univ. Oslo, Oslo, 1977) Studies in Logic and the Foundations of Mathematics, vol. 94, North-Holland, Amsterdam-New York, 1978, pp. 185–222. MR 516936
- S. C. Kleene, Recursive functionals and quantifiers of finite types revisited. II, The Kleene Symposium (Proc. Sympos., Univ. Wisconsin, Madison, Wis., 1978), Studies in Logic and the Foundations of Mathematics, vol. 101, North-Holland, Amsterdam-New York, 1980, pp. 1–29. MR 591873
- S. C. Kleene, Recursive functionals and quantifiers of finite types revisited. III, Patras Logic Symposion (Patras, 1980) Studies in Logic and the Foundations of Mathematics, vol. 109, North-Holland, Amsterdam-New York, 1982, pp. 1–40. MR 694251 Sympos. Pure Math, (from the American Mathematical Society’s 1982 Summer Research Institute on Recursion Theory at Cornell University, June 27-July 16) (A. Nerode, ed.), vol. 42, Amer. Math. Soc., Providence, R.I., pp. 119-138.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 325 (1991), 593-630
- MSC: Primary 03D65
- DOI: https://doi.org/10.1090/S0002-9947-1991-0974519-8
- MathSciNet review: 974519