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References

  1. Bergstra, J.A.: Computability and continuity in finite types. Theses, University of Utrecht 1976.

  2. Bergstra, J.A.: The continuous functionals and2 E. In: Fenstad, J.E., Gandy, R.O., Sacks, G.E. (eds.): Generalized recursion theory. II. Amsterdam: North-Holland 1978.

    Google Scholar 

  3. Grilliot, T.: On effectively discontinuous type-2 objects, J. Symb. Logic36, 245–248 (1971).

    Google Scholar 

  4. Hyland, J.M.E.: Filterspaces and continuous functionals. Ann. Math. Logic16, 101–143 (1979).

    Article  Google Scholar 

  5. Kleene, S.C.: Recursive functionals and quantifiers of finite types. I. Trans. Am. Math. Soc.91 1–52 (1959); II, 106–142 (1963).

    Google Scholar 

  6. Kleene, S.C.: Countable functionals. In: Heyting, A. (ed.): Constructivity in mathematics, pp. 81–100. Amsterdam: North-Holland 1959.

    Google Scholar 

  7. Kreisel, G.: Interpretation of analysis by means of functionals of finite type. In: Heyting, A. (ed.): Constructivity in mathematics, pp. 101–128. Amsterdam: North-Holland 1959.

    Google Scholar 

  8. Normann, D.: Recursion on the continuous functionals. In: Springer Lecture Notes. Berlin, Heidelberg, New York: Springer 1980.

    Google Scholar 

  9. Normann, D.: The continuous functionals; computations, recursions, and degrees. Ann. Math. Logic21, 1–26 (1981).

    Article  Google Scholar 

  10. Normann, D.: General typestructures of continuous and countable functionals (to appear in Arch. math. Logik).

  11. Normann, D.: Characterizing the continuous functionals (to appear in J. Symb. Logic).

  12. Normann, D., Wainer, S.S.: The 1-section of a countable functional. J. Symb. Logic45, 549–562 (1980).

    Google Scholar 

  13. Soare, R.I.: Fundamental methods for constructing recursively enumerable degrees. In: Drake, F.R., Wainer, S.S., (eds.): Recursion theory: its generalisations and applications, pp. 1–51. Cambridge: Cambridge University Press 1980.

    Google Scholar 

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Normann, D. R.E. degrees of continuous functionals. Arch math Logik 23, 79–98 (1983). https://doi.org/10.1007/BF02023015

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  • DOI: https://doi.org/10.1007/BF02023015

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