This article is cited in 8 papers

Brief communications

Splitting of 2-computably enumerable degrees with avoiding cones

M. M. Yamaleev

Chair of Algebra and Mathematical Logic, Kazan State University, Kazan, Russia

Abstract: In this paper we show that for any pair of properly 2-c. e. degrees $\mathbf0<\mathbf d<\mathbf a$ such that there are no c. e. degrees between $\mathbf d$ and $\mathbf a$, the degree $\mathbf a$ is splittable in the class of 2-c. e. degrees avoiding the upper cone of $\mathbf d$. We also study the possibility to characterize such an isolation in terms of splitting.

Keywords: 2-c. e. degrees, Turing degrees, splitting, splitting with avoiding cones, isolation.

UDC: 510.532

Received: 16.12.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:6, 63–66

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