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Hierarchies over recursive well-orderings

Published online by Cambridge University Press:  12 March 2014

Herbert Enderton  and
David Luckham
Herbert Enderton
Affiliation:
Massachusetts Institute of Technology
David Luckham
Affiliation:
Massachusetts Institute of Technology
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Extract

In the original example of a transfinite hierarchy of degrees of unsolvability, a predicate Ha is associated with each a in the set 0 of ordinal notations. (See Kleene [K1], Spector [S1], and the references there to Davis and Mostowski.) The predicates are defined by means of induction over the partial well-ordering relation ≤0 on the set 0 of notations for the recursive ordinals. The usefulness of this hierarchy of predicates is enhanced by Spector's proof [S1] of the “uniqueness” property: viz. that the degree of Ha depends only on the ordinal |a| for which a is a notation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 29 , Issue 4 , December 1964 , pp. 183 - 190
Copyright
Copyright © Association for Symbolic Logic 1964

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References

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