The Journal of Symbolic Logic

Research Article

Degrees of unsolvability of constructible sets of integers

George Boolosa1a2 and Hilary Putnama2

a1 Columbia University

a2 Harvard University

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

(Received August 22 1966)

(Revised December 08 1967)