Pointwise decomposable sets

G. N. Kobzev

Matematičeskie zametki, Tome 13 (1973) no. 6, pp. 893-898

Résumé

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 $\overline C=\{c_0<c_1<c_2<\dots\}$.