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A note on the hyperarithmetical hierarchy

Published online by Cambridge University Press:  12 March 2014

H. B. Enderton  and
Hilary Putnam
H. B. Enderton
Affiliation:
University of California, Los Angeles
Hilary Putnam
Affiliation:
Harvard University
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Extract

The hyperarithmetical hierarchy assigns a degree of unsolvability hγ to each constructive ordinal γ. This assignment has the properties that h0 is the recursive degree and hγ+1 is the jump h′γ of hγ. For a limit ordinal λ < ω1 it is not so easy to define hγ. The original definitions used systems of notations for ordinals, see Spector [6]. There are also later notation-free definitions due to Shoenfield (unpublished) and to Hensel and Putnam [4].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 3 , September 1970 , pp. 429 - 430
Copyright
Copyright © Association for Symbolic Logic 1971

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References

[1]Boyd, R., Hensel, G., and Putnam, H., A recursion-theoretic characterization of the ramified analytical hierarchy, Transactions of the American Mathematical Society, vol. 141 (1969), pp. 37–62.CrossRefGoogle Scholar
[2]Gandy, R. O., On a problem of Kleene's, Bulletin of the American Mathematical Society, vol. 66 (1960), pp. 501–502.CrossRefGoogle Scholar
[3]Gandy, R., Kreisel, G., and Tait, W., Set existence, Bulletin de l' Académie Polonaise des Sciences, Série des sciences mathématiques, astronomiques et physiques, vol. 8 (1960), pp. 577–582.Google Scholar
[4]Hensel, G. and Putnam, H., On the notational independence of various hierarchies of degrees of unsolvability, this Journal, vol. 30 (1965), pp. 69–86.Google Scholar
[5]Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill, 1967.Google Scholar
[6]Spector, C., Recursive well-orderings, this Journal, vol. 20 (1955), pp. 151–163.Google Scholar
[7]Spector, C., On degrees of recursive unsolvability, Annals of mathematics, vol. 64 (1956), pp. 581–592.CrossRefGoogle Scholar