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Matematicheskie Zametki, 1973, Volume 13, Issue 6, Pages 893–898 (Mi mzm7194)  

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
English version:
Mathematical Notes, 1973, Volume 13, Issue 6, Pages 533–536
DOI: https://doi.org/10.1007/BF01163964
Bibliographic databases:
UDC: 518
Language: Russian
Citation: G. N. Kobzev, “Pointwise decomposable sets”, Mat. Zametki, 13:6 (1973), 893–898; Math. Notes, 13:6 (1973), 533–536
Citation in format AMSBIB
\Bibitem{Kob73}
\by G.~N.~Kobzev
\paper Pointwise decomposable sets
\jour Mat. Zametki
\yr 1973
\vol 13
\issue 6
\pages 893--898
\mathnet{http://mi.mathnet.ru/mzm7194}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=329874}
\zmath{https://zbmath.org/?q=an:0292.02036}
\transl
\jour Math. Notes
\yr 1973
\vol 13
\issue 6
\pages 533--536
\crossref{https://doi.org/10.1007/BF01163964}
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