Geodesic
A generic relation on recursively enumerable sets
Algebra i logika, Tome 55 (2016) no. 5, pp. 587-596

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We introduce the concept of a generic relation for algorithmic problems, which preserves the property of being decidable for a problem for almost all inputs and possesses the transitive property. As distinct from the classical $m$-reducibility relation, the generic relation under consideration does not possess the reflexive property: we construct an example of a recursively enumerable set that is generically incomparable with itself. We also give an example of a set that is complete with respect to the generic relation in the class of recursively enumerable sets.
Keywords: generic relation, complete set, recursively enumerable set. 
@article{AL_2016_55_5_a4,
     author = {A. N. Rybalov},
     title = {A~generic relation on recursively enumerable sets},
     journal = {Algebra i logika},
     pages = {587--596},
     publisher = {mathdoc},
     volume = {55},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2016_55_5_a4/}
}
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A. N. Rybalov. A generic relation on recursively enumerable sets. Algebra i logika, Tome 55 (2016) no. 5, pp. 587-596. http://geodesic.mathdoc.fr/item/AL_2016_55_5_a4/