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Priority arguments in the continuous r.e. degrees1

Published online by Cambridge University Press:  12 March 2014

Simon Thompson
Simon Thompson*
Affiliation:
Computing Laboratory, University of Kent at Canterbury, Canterbury, Kent, England
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Abstract

We show that at each type κ ≥ 2, there exist c-irreducible functionals of c-r.e. degree, as defined in [Nor 1]. Our proofs are based on arguments due to Hinman, [Hin 1], and Dvornikov, [Dvo 1].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 50 , Issue 3 , September 1985 , pp. 661 - 667
Copyright
Copyright © Association for Symbolic Logic 1985

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Footnotes

1

Research partially supported by a Science and Engineering Research Council Studentship.

References

REFERENCES

[Dvo 1]Dvornikov, S. G., On C-degrees of continuous, everywhere defined functionals, Algebra i Logika, vol. 18 (1979), pp. 32–46; English translation, Algebra and Logic, vol. 18 (1979), pp. 21–31.Google Scholar
[GaH 1]Gandy, R. O. and Hyland, J. M. E., Compatible and recursively countable functions of higher type, Logic Colloquium '76 (Gandy, R. O. and Hyland, J. M. E., editors), North-Holland, Amsterdam, 1977, pp. 407–438.Google Scholar
[Hin 1]Hinman, P. G., Degrees of continuous functionals, this Journal, vol. 38 (1973), pp. 393–395.Google Scholar
[Nor 1]Normann, D., R.e. degrees of continuous functionals, Archiv für Mathematische Logik und Grundlagenforschung, vol. 23 (1983), pp. 79–98.CrossRefGoogle Scholar
[Nor 2]Normann, D., Recursion on the countable functionals, Lecture Notes in Mathematics, vol. 811, Springer-Verlag, Berlin, 1980.CrossRefGoogle Scholar
[Sho 1]Shoenfield, J. R., Degrees of unsolvability, North-Holland, Amsterdam, 1971.Google Scholar
[Tho 1]Thompson, S. J., Recursion theories on the continuous functionals, D. Phil. Thesis, Oxford University, Oxford, 1984.Google Scholar