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Some jump-like operations in β-recursion theory

Published online by Cambridge University Press:  12 March 2014

Colin G. Bailey
Colin G. Bailey*
Affiliation:
School of Mathematics, Statistics & Operations Research, Victoria University of Wellington, Wellington, New Zealand, E-mail: [email protected]
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Abstract

In this paper we show that there are various pseudo-jump operators definable over inadmissible Jβ that relate to the failure of admissiblity and to non-regularity. We will use these ideas to construct some intermediate degrees.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 57 - 71
Copyright
Copyright © Association for Symbolic Logic 2013

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References

REFERENCES

[1]Devlin, K., Constructibility, Springer-Verlag, Berlin, 1984.CrossRefGoogle Scholar
[2]Friedman, S. D., β-recursion theory, Transactions of the American Mathematical Society, vol. 255 (1979), pp. 173–200.Google Scholar
[3]Friedman, S. D., Negative solutions to Post's problem. II, Annals of Mathematics, vol. 113 (1981), pp. 25–43.CrossRefGoogle Scholar
[4]Homer, S., Intermediate β-r.e. degrees and the half-jump, this Journal, vol. 48 (1983), pp. 790–796.Google Scholar
[5]Maass, W., Inadmissibility, tame r.e. sets and the admissible collapse, Annals of Mathematical Logic, vol. 13 (1978), pp. 149–170.CrossRefGoogle Scholar
[6]Stanley, L. J., A short course on gap-one morasses with a review of the fine structure of L, Surveys in set theory (Mathias, A. R. D., editor), London Mathematical Society Lecture Note Series, vol. 87, Cambridge University Press, Cambridge, 1983, pp. 197–243.CrossRefGoogle Scholar