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Recursion in 3 E and a Splitting Theorem

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Essays on Mathematical and Philosophical Logic

Part of the book series: Synthese Library ((SYLI,volume 122))

Abstract

In this paper we will make a survey of some results concerning recursion in a normal type-3-object as defined by Kleene [6]. We will use an alternative definition originally described in Normann [10] where we extend recursion theory to arbitrary sets.

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References

  1. K. Devlin, Aspects of Constructibility, Springer Lecture Notes 354.

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  2. J. E. Fenstad, ‘Computation theories: An axiomatic approach to recursion on general structures’, in Müller, Obeischelp and Potthoff (eds.), Logic Conference, Kiel 1974, 143–169, Springer Lecture Notes 499.

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  3. J. E. Fenstad, monograph on recursion theory, in preparation.

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  6. S. C. Kleene, ‘Recursive functionals and quantifiers of finite type I’, Trans. Amer. Math. Soc. 91 (1959), 1–52, and II, 108 (1963), 106-142.

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  7. D. B. MacQueen, Post’s Problem for Recursion in Higher Types, Ph.D. Thesis, MIT, 1972.

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  8. J. Moldestad, ‘Computation Theory on Two Types’, Preprint Series no. 2, Oslo, 1976.

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  10. D. Normann, ‘Degrees of functionals’, Preprint Series no. 22, Oslo, 1975.

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  11. G. E. Sacks, ‘The 1-section of a type n object’, in Fenstad and Hinman (eds.), Generalized recursion theory, 81–93, North-Holland, 1974.

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  12. G. E. Sacks, ‘The k-section of a type n object’, to appear.

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© 1979 D. Reidel Publishing Company, Dordrecht, Holland

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Normann, D. (1979). Recursion in 3 E and a Splitting Theorem. In: Hintikka, J., Niiniluoto, I., Saarinen, E. (eds) Essays on Mathematical and Philosophical Logic. Synthese Library, vol 122. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9825-4_14

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  • DOI: https://doi.org/10.1007/978-94-009-9825-4_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-9827-8

  • Online ISBN: 978-94-009-9825-4

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