×

R.e. degrees of continuous functionals. (English) Zbl 0527.03028


MSC:

03D65 Higher-type and set recursion theory
03D25 Recursively (computably) enumerable sets and degrees

Citations:

Zbl 0472.03037
PDFBibTeX XMLCite
Full Text: DOI EuDML

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.
[3] Grilliot, T.: On effectively discontinuous type-2 objects, J. Symb. Logic36, 245–248 (1971). · Zbl 0224.02034 · doi:10.2307/2270259
[4] Hyland, J.M.E.: Filterspaces and continuous functionals. Ann. Math. Logic16, 101–143 (1979). · Zbl 0415.03037 · doi:10.1016/0003-4843(79)90006-8
[5] Kleene, S.C.: Recursive functionals and quantifiers of finite types. I. Trans. Am. Math. Soc.91 1–52 (1959); II, 106–142 (1963). · Zbl 0088.01301
[6] Kleene, S.C.: Countable functionals. In: Heyting, A. (ed.): Constructivity in mathematics, pp. 81–100. Amsterdam: North-Holland 1959. · Zbl 0100.24901
[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.
[8] Normann, D.: Recursion on the continuous functionals. In: Springer Lecture Notes. Berlin, Heidelberg, New York: Springer 1980. · Zbl 0439.03028
[9] Normann, D.: The continuous functionals; computations, recursions, and degrees. Ann. Math. Logic21, 1–26 (1981). · Zbl 0472.03037 · doi:10.1016/0003-4843(81)90014-0
[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). · Zbl 0536.03026
[12] Normann, D., Wainer, S.S.: The 1-section of a countable functional. J. Symb. Logic45, 549–562 (1980). · Zbl 0439.03029 · doi:10.2307/2273422
[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.