Geodesic
Noncancellable, singular, and conjugate degrees
Algebra i logika, Tome 56 (2017) no. 3, pp. 275-299

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We study degree structures of stronger algorithmic reducibilities inside the degrees of weaker algorithmic ones. Results in this area are reviewed for algorithmic reducibilities $m$-, $1$-, $tt$-, $wtt$-, $T$-, $e$-, $s$-, $Q$-, and we formulate questions that are still not settled for these. A computably enumerable $Q$-degree which consists of one computably enumerable $m$-degree is constructed.
Keywords: $Q$-reducibility, $m$-reducibility, computably enumerable degrees, noncancellable degrees, singular degrees, conjugate degrees. 
@article{AL_2017_56_3_a0,
     author = {I. I. Batyrshin},
     title = {Noncancellable, singular, and conjugate degrees},
     journal = {Algebra i logika},
     pages = {275--299},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_3_a0/}
}
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I. I. Batyrshin. Noncancellable, singular, and conjugate degrees. Algebra i logika, Tome 56 (2017) no. 3, pp. 275-299. http://geodesic.mathdoc.fr/item/AL_2017_56_3_a0/