Abstract:
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.
Citation:
S. A. Badaev, B. S. Kalmurzayev, N. K. Mukash, A. A. Khamitova, “Special classes of positive preorders”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1657–1666