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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 There are also later notation-free definitions due to Shoenfield (unpublished) and to Hensel and Putnam [4].

Information

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

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