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Open AccessJournal ArticleDOI

The continuity of cupping to 0

Klaus Ambos-Spies, +2 more
- 11 Nov 1993 - 
- Vol. 64, Iss: 3, pp 195-209
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TLDR
It is shown that, if a, b are recursively enumerable degrees such that 0 a a ∪ b = 0', then there exists a recursically enumerable degree c such that c a and c ∪b = 0'.
About: 
This article is published in Annals of Pure and Applied Logic.The article was published on 1993-11-11 and is currently open access. It has received 18 citations till now. The article focuses on the topics: Recursively enumerable language & Degree (graph theory).

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Book ChapterDOI

Games in Recursion Theory and Continuity Properties of Capping Degrees

Leo Harrington, +1 more
TL;DR: In this paper, it was shown that there are no maximal minimal pairs of recursively enumerable (r.e.) degrees, R, which hold continuously in a neighborhood about a and b.
Journal Article

Universal cupping degrees

Angsheng Li, +2 more
- 01 Jan 2006 - 
TL;DR: The cupping/noncupping properties were able to employ to show that the theory of the c.e. degrees under relation ≤ is undecidable, and cuppable and noncuppable degrees were further studied.
Journal ArticleDOI

Coherence in SMCCs and equivalences on derivations in IMLL with unit

Laurent Mehats, +1 more
- 01 Jul 2007 - 
TL;DR: It is established that any equivalence induced by the equality of canonical natural transformations over a model can be axiomatized by some set of “critical” pairs of derivations, and certain sufficient conditions for full coherence are derived.
Journal ArticleDOI

Relative enumerability and 1-genericity

Wei Wang
- 01 Sep 2011 - 
TL;DR: It is shown that if b is c.e.a. c then b is b if and only if b and c respectively contain B and C as above.
Book ChapterDOI

Universal cupping degrees

Angsheng Li, +2 more
TL;DR: In this paper, it was shown that the theory of nonzero computably enumerable (c.e. for short) degrees under relation ≤ is undecidable, and the existence of non-cupping degrees is shown to be a non-trivial problem.
References
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Journal ArticleDOI

Recursively enumerable sets and degrees

Robert I. Soare
- 01 Mar 1987 - 
TL;DR: In this paper, the relation of the structure of an R set to its degree is discussed, and the infinite injury priority method is proposed to solve the problem of scaling and splitting R sets.
Journal ArticleDOI

An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees

Klaus Ambos-Spies, +3 more
- 01 Jan 1984 - 
TL;DR: In this article, a decomposition definissable du semi-treillis superieur des degres recursivement enumerables R comme l'union disjointe d'un ideal M and un filtre fort NC is defined.
Book ChapterDOI

Games in Recursion Theory and Continuity Properties of Capping Degrees

Leo Harrington, +1 more
TL;DR: In this paper, it was shown that there are no maximal minimal pairs of recursively enumerable (r.e.) degrees, R, which hold continuously in a neighborhood about a and b.