COMPUTABLE REDUCIBILITY FOR COMPUTABLE LINEAR ORDERS OF TYPE [omega]

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 [OMEGA]. We show that, over an arbitrary degree from [OMEGA], there exists an infinite antichain of self-full degrees. This fact implies that the poset [OMEGA] has continuum many automorphisms. We prove that any non-self-full degree from [OMEGA] has no minimal covers, which implies that, inside [OMEGA], the self-full degrees are precisely those elements that have a minimal cover. Bibliography: 18 titles.