2022
DOI: 10.1007/s10958-022-06148-5
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Computable Reducibility for Computable Linear Orders of Type ω

Abstract: 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 … Show more

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Cited by 2 publications
(2 citation statements)
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“…Also, in [10] it was proved that there is no strong minimal cover for a non-self-full degree. This Moreover, in [11] it was proved that there exists an antichain of self-full degrees above any given degree…”
Section: Main Provisions Materials and Methodsmentioning
confidence: 91%
See 1 more Smart Citation
“…Also, in [10] it was proved that there is no strong minimal cover for a non-self-full degree. This Moreover, in [11] it was proved that there exists an antichain of self-full degrees above any given degree…”
Section: Main Provisions Materials and Methodsmentioning
confidence: 91%
“…The papers [11,12] studied the following structure: 𝛀𝛀 = ({deg 𝑐𝑐 (𝐿𝐿): 𝐿𝐿 is a computable linear order isomorphic to 𝜔𝜔 𝑠𝑠𝑠𝑠 }; ≤ 𝑐𝑐 ) Moreover, in [11] it was proved that there exists an antichain of self-full degrees given degree 𝒂𝒂 ∈ 𝛀𝛀. This fact implies that the structure 𝛀𝛀 has continuum many autom Also, in [10] it was proved that there is no strong minimal cover for a non-self-full de has continuum many automorphisms.…”
Section: Main Provisions Materials and Methodsmentioning
confidence: 99%