On the distribution of Lachlan nonsplitting bases

On the distribution of Lachlan nonsplitting bases

We say that a computably enumerable (c.e.) degree b is a Lachlan nonsplitting base (LNB), if there is a computably enumerable degree a such that a is greater than b, and for any c.e. degrees w,v h a, if a h w or; v or; b then either a h w or; b or a h v or; b. In this paper we investigate the relati...

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Bibliographic Details
Published in:Archive for mathematical logic Vol. 41; no. 5; pp. 455 - 482
Main Authors: Cooper, S. Barry, Li, Angsheng, Yi, Xiaoding
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01-07-2002
Subjects:
Fuzzy logic
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Summary:We say that a computably enumerable (c.e.) degree b is a Lachlan nonsplitting base (LNB), if there is a computably enumerable degree a such that a is greater than b, and for any c.e. degrees w,v h a, if a h w or; v or; b then either a h w or; b or a h v or; b. In this paper we investigate the relationship between bounding and nonbounding of Lachlan nonsplitting bases and the high/low hierarchy. We prove that there is a non-Low2 c.e. degree which bounds no Lachlan nonsplitting base. [PUBLICATION ABSTRACT]
ISSN:0933-5846
1432-0665
DOI:10.1007/s001530100095