Geodesic
On $tt$-degrees of recursively enumerable Turing degrees
Sbornik. Mathematics, Tome 35 (1979) no. 2, pp. 173-180 
G. N. Kobzev. On $tt$-degrees of recursively enumerable Turing degrees. Sbornik. Mathematics, Tome 35 (1979) no. 2, pp. 173-180. http://geodesic.mathdoc.fr/item/SM_1979_35_2_a1/
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     title = {On~$tt$-degrees of recursively enumerable {Turing} degrees},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The main result of the paper asserts that if $A$ is a semirecursive $\eta$-hyperhypersimple set, then for every set $B$ with $A\equiv_TB$ there exists a recursive set $C$ such that $C\leq_mA$ and $C\leqslant_{tt}B$. If $B$ is recursively enumerable, then $C\leqslant_qB$. A corollary asserts that if a $tt$-degree contains an $\eta$-maximal semirecursive set, then it is a minimal element in the semilattice of all $tt$-degrees. Bibliography: 9 titles.

[1] X. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, izd-vo “Mir”, Moskva, 1972 | MR

[2] N. G. Kobzev, $btt$-svodimost, Kandidatskaya dissertatsiya, Novosibirsk, 1975

[3] G. N. Kobzev, “O $r$-otdelimykh mnozhestvakh”, Issledovaniya po matematicheskoi logike i teorii algoritmov, Institut prikladnoi matematiki, Tbil. un-t, 1975, 19–30 | MR

[4] C. G. Jockusch Jr., “Semirecursive sets and positive reducibility”, Trans. Amer. Math. Soc., 131 (1968), 420–436 | DOI | MR | Zbl

[5] S. S. Marchenkov, “Ob odnom klasse nepolnykh mnozhestv”, Matem. zametki, 20:4 (1976), 473–478 | MR | Zbl

[6] S. Kallibekov, “Indeksnye mnozhestva stepenei nerazreshimosti”, Algebra i logika, 10:3 (1971), 316–326 | MR | Zbl

[7] A. N. Degtev, “Nasledstvennye mnozhestva i tablichnaya svodimost”, Algebra i logika, 11:3 (1972), 257–269 | MR | Zbl

[8] A. N. Degtev, “O $tt$- i $m$-stepenyakh”, Algebra i logika, 12:2 (1973), 143–161 | MR | Zbl

[9] S. S. Marchenkov, “O suschestvovanii rekursivno-perechislimykh minimalnykh tablichnykh stepenei”, Algebra i logika, 14:4 (1975), 422–429 | MR | Zbl