Geodesic
Special classes of positive preorders
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1657-1666

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We study positive preorders relative to computable reducibility. An approach is suggested to lift well-known notions from the theory of ceers to positive preorders. It is shown that each class of positive preoders of a special type (precomplete, $e$-complete, weakly precomplete, effectively finite precomplete, and effectively inseparable ones) contains infinitely many incomparable elements and has a universal object. We construct a pair of incomparable dark positive preorders that possess an infimum. It is shown that for every non-universal positive preorder $P$, there are infinitely many pairwise incomparable minimal weakly precomplete positive preorders that are incomparable with $P$.
Keywords: positive preorder, ceer, computable reducibility, precomplete, weakly precomplete, minimal preorder. 
@article{SEMR_2021_18_2_a14,
     author = {S. A. Badaev and B. S. Kalmurzayev and N. K. Mukash and A. A. Khamitova},
     title = {Special classes of positive preorders},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1657--1666},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a14/}
}
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S. A. Badaev; B. S. Kalmurzayev; N. K. Mukash; A. A. Khamitova. Special classes of positive preorders. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1657-1666. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a14/