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Pointwise decomposable sets
G. N. Kobzev Novosibirsk State University
Abstract:
We show that, under the conditional $a'<0''$, every recursively enumerable (r.e.) $A\in a$ has a pointwise decomposable complement. If $A\le{}_TB$, $A$ and $\overline B$ are r.e. co-retraceable sets, and $f(x)=f^B(x)$, then there exists a r.e. co-retraceable $C$, such that $A\subset C$, $B\equiv{}_TC$, ($\forall n$) ($f(n)<c_n$), where $\overline C=\{c_0<c_1<c_2<\dots\}$.
Received: 10.05.1972
Citation:
G. N. Kobzev, “Pointwise decomposable sets”, Mat. Zametki, 13:6 (1973), 893–898; Math. Notes, 13:6 (1973), 533–536
Linking options:
https://www.mathnet.ru/eng/mzm7194 https://www.mathnet.ru/eng/mzm/v13/i6/p893
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