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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 4, Pages 3–9
(Mi ivm6720)
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This article is cited in 3 scientific papers (total in 3 papers)
Isolated 2-computably enumerable $Q$-degrees
I. I. Batyrshin Chair of Algebra and Mathematical Logic, Kazan State University, Kazan, Russia
Abstract:
We demonstrate that for every pair of computably enumerable degrees $\mathbf a<_\mathbf Q\mathbf b$ there exists a properly 2-computably enumerable degree $\mathbf d$, $\mathbf a<_\mathbf Q\mathbf d<_\mathbf Q\mathbf b$, such that $\mathbf a$ isolates $\mathbf d$ from below and $\mathbf b$ isolates $\mathbf d$ from above. As a corollary we prove that there exists a 2-computably enumerable degree which is $Q$-incomparable with any nontrivial (i.e., different from $\boldsymbol0$ and $\boldsymbol0'$) computably enumerable degree, and that every nontrivial computably enumerable degree isolates some 2-computably enumerable degree from below and some 2-computably enumerable degree from above.
Keywords:
computably enumerable sets, quasi-reducibility, 2-computably enumerable sets, isolated degrees.
Received: 03.03.2008
Citation:
I. I. Batyrshin, “Isolated 2-computably enumerable $Q$-degrees”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 4, 3–9; Russian Math. (Iz. VUZ), 54:4 (2010), 1–6
Linking options:
https://www.mathnet.ru/eng/ivm6720 https://www.mathnet.ru/eng/ivm/y2010/i4/p3
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Abstract page: | 369 | Full-text PDF : | 68 | References: | 54 | First page: | 6 |
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