The degrees of hyperhyperimmune sets-Reference-Cited by-同舟云学术

The degrees of hyperhyperimmune sets

Published:1969-11-17 Issue:3 Volume:34 Page:489-493
ISSN:0022-4812
Container-title:Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

Jockusch Carl G.

Abstract

In [5, Corollary 3.1] D. A. Martin characterized the degrees of the hyperhypersimple sets as those r.e. degrees a satisfying a′ = 0″. In the present paper we investigate the degrees of the hyperhyperimmune (h.h.i.) sets. We do not achieve a characterization of these degrees, but we do show that the condition a′ ≥ 0″ is sufficient, and the condition a′ ≥ 0′ is necessary, for a degree a to contain an h.h.i. set.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference12 articles.

1. A theoremon minimal degrees;Shoenfield;this Journal,1966

2. On Degrees of Unsolvability

3. A theorem on hyperhypersimple sets;Martin;this Journal,1963

4. Jockusch C. G. Jr. and McLaughlin T. G. , Countable retracing functions and Π2 0 predicates, Pacific journal of mathematics (to appear).

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