Abstract
LetA be a subset of\(\mathbb{N} = \{ 0,1,2,...\} \), and leta∉A. The setA is said to be almost semirecursive, if there is a two-place general recursive functionf such thatf(x, y)ε{x, y, a}∧({x, y}⊆A⇌f(x, y)εA) for all\(x,y \in \mathbb{N}\). Among other facts, it is proved that ifA and\(\mathbb{N}\backslash A\) are almost semirecursive sets, thenA is a semirecursive set, and that there exists a wsr*-set that is neither a wsr-nor an almost semirecursive set.
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Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 188–193, August, 1999.
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Degtev, A.N. Almost semirecursive sets. Math Notes 66, 148–152 (1999). https://doi.org/10.1007/BF02674870
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DOI: https://doi.org/10.1007/BF02674870