George Boolos and Hilary Putnam. Degrees of unsolvability of constructible sets of integers. The journal of symbolic logic, vol. 33 no. 4 (for 1968, pub. 1969), pp. 497–513.

1973 ◽  
Vol 38 (3) ◽  
pp. 527-528
Author(s):  
A. S. Kechris
Keyword(s):  
Hilary Putnam ◽  
Symbolic Logic ◽  
Constructible Sets ◽  
George Boolos ◽  
Degrees Of Unsolvability

Degrees of unsolvability of constructible sets of integers

1969 ◽  
Vol 33 (4) ◽  
pp. 497-513 ◽  
Author(s):  
George Boolos ◽  
Hilary Putnam
Keyword(s):  
Fine Structure ◽  
Continuum Hypothesis ◽  
Arithmetical Hierarchy ◽  
Constructible Sets ◽  
Degrees Of Unsolvability ◽  
The Continuum

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

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