Weakly semirecursive sets

Journal of Symbolic Logic 55 (2):637-644 (1990)
Abstract
We introduce the notion of "semi-r.e." for subsets of ω, a generalization of "semirecursive" and of "r.e.", and the notion of "weakly semirecursive", a generalization of "semi-r.e.". We show that A is weakly semirecursive iff, for any n numbers x 1 ,...,x n , knowing how many of these numbers belong to A is equivalent to knowing which of these numbers belong to A. It is shown that there exist weakly semirecursive sets that are neither semi-r.e. nor co-semi-r.e. On the other hand, we exhibit nonzero Turing degrees in which every weakly semirecursive set is semirecursive. We characterize the notion "A is weakly semirecursive and recursive in K" in terms of recursive approximations to A. We also show that if a finite Boolean combination of r.e. sets is semirecursive then it must be r.e. or co-r.e. Several open questions are raised
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DOI 10.2307/2274653
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References found in this work BETA
Nondeterministic Bounded Query Reducibilities.Richard Beigel, William Gasarch & Jim Owings - 1989 - Annals of Pure and Applied Logic 41 (2):107-118.

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Citations of this work BETA
Weakly Semirecursive Sets and R.E. Orderings.Martin Kummer & Frank Stephan - 1993 - Annals of Pure and Applied Logic 60 (2):133-150.

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