Splitting and nonsplitting, II: A low2 c.e. degree above which 0′ is not splittable

Author:

Cooper S. Barry,Li Angsheng

Abstract

AbstractIt is shown that there exists a low2 Harrington non-splitting base — that is, a low2 computably enumerable (c.e.) degree a such that for any c.e. degrees x, y, if 0 = xy, then either 0 = xa or 0 = ya. Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the low2-ness requirements to be satisfied, and the proof given involves new techniques with potentially wider application.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference15 articles.

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Splitting and jump inversion in the Turing degrees;Computability;2018-06-07

2. S. Barry Cooper (1943–2015);Computability;2018-06-07

3. Elementary differences among jump classes;Theoretical Computer Science;2009-03

4. On Lachlan’s major sub-degree problem;Archive for Mathematical Logic;2008-06-27

5. A join theorem for the computably enumerable degrees;Transactions of the American Mathematical Society;2004-02-27

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