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Degrees of unsolvability of constructible sets of integers

Published online by Cambridge University Press:  12 March 2014

George Boolos  and
Hilary Putnam
George Boolos
Affiliation:
Columbia University Harvard University
Hilary Putnam
Affiliation:
Harvard University
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Extract

Why the Post-Kleene arithmetical hierarchy of degrees of (recursive) unsolvability was extended into the transfinite is not clear. Perhaps it was thought that if a hierarchy of sufficiently fine structure could be described that would include all sets of integers, some light might be thrown on the Continuum Hypothesis, and its truth or falsity possibly even ascertained. There is also some evidence in the 1955 papers of Kleene (cf. Kleene [2], [3], [4]) that it was once hoped that a theorem for the analytical hierarchy analogous to the result of Post and Kleene

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 4 , January 1969 , pp. 497 - 513
Copyright
Copyright © Association for Symbolic Logic 1969

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