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Splitting and Decomposition by Regressive Sets, II

Published online by Cambridge University Press:  20 November 2018

T. G. McLaughlin
T. G. McLaughlin*
Affiliation:
University of Illinois, Urbana, III
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In (3), Dekker drew attention to an analogy between (a) the relationship of the recursive sets to the recursively enumerable sets, and (b) the relationship of the retraceable sets to the regressive sets. As was to be expected, this analogy limps in some respects. For example, if a number set α is split by a recursive set, then it is decomposed by a pair of recursively enumerable sets; whereas, as we showed in (6, Theorem 2), α may be split by a retraceable set and yet not decomposable (in a liberal sense of the latter term) by a pair of regressive sets. The result for recursive and recursively enumerable sets, of course, follows from the trivial fact that the complement of a recursive set is recursive.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 291 - 311
Copyright
Copyright © Canadian Mathematical Society 1967

References

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