Computable Reducibility for Computable Linear Orders of Type ω

Askarbekkyzy A. Bazhenov N.A. Kalmurzayev B.S.
November 2022 Springer

Journal of Mathematical Sciences (United States)
2022 #267 Issue 4 429 - 443 pp.

We study computable reducibility for computable isomorphic copies of the standard ordering of natural numbers. Following Andrews and Sorbi, we isolate the class of self-full degrees inside the induced degree structure Ω. We show that, over an arbitrary degree from Ω, there exists an infinite antichain of self-full degrees. This fact implies that the poset Ω has continuum many automorphisms. We prove that any non-self-full degree from Ω has no minimal covers, which implies that, inside Ω, the self-full degrees are precisely those elements that have a minimal cover.

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Kazakh-British Technical University, 59, Tole bi St., Almaty, 050000, Kazakhstan
Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr., Novosibirsk, 630090, Russian Federation
Al-Farabi Kazakh National University, 71, Al-Farabi pr., Almaty, 050040, Kazakhstan

Kazakh-British Technical University
Sobolev Institute of Mathematics SB RAS
Al-Farabi Kazakh National University

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