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Uniformly introreducible sets1

Published online by Cambridge University Press:  12 March 2014

Carl G. Jockusch Jr.
Carl G. Jockusch Jr.*
Affiliation:
Northeastern University and Massachusetts Institute of Technology
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Retraceable sets were denned in Dekker and Myhill [5]. In that paper it was pointed out that if A is a retraceable set, then A is recursive in each of its infinite subsets, i.e. A is introreducible. We would like to know to what extent theorems on retraceable sets also hold for introreducible sets; however, we have made very little progress in this direction. On the other hand, “uniformly introreducible” sets (which will be defined in §2) are more tractable, and it turns out that some results on retraceable sets extend to uniformly introreducible sets while others fail.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 4 , January 1969 , pp. 521 - 536
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

This research was supported in part by National Science Foundation Grant GP 4361 at M.I.T. The author is grateful to the referee and T. G. McLaughlin for helpful suggestions.

References

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