Abstract
We show that, under the conditionala′<0″, every recursively enumerable (r.e.) Aε bia has a pointwise decomposable complement. If A ≤ TB, A and ¯B are r.e. co-retraceable sets, and f(x)=fB(x), then there exists a r.e. co-retraceable C, such thatA∼(c),B≡T C, (A n) (f(n) <c n), where ¯C=C 0<C 1<C 2<....
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Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 893–898, June, 1973.
The author thanks A. N. Degtev for his interest in this work.
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Kobzev, G.N. Pointwise decomposable sets. Mathematical Notes of the Academy of Sciences of the USSR 13, 533–536 (1973). https://doi.org/10.1007/BF01163964
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DOI: https://doi.org/10.1007/BF01163964