On the distribution of Lachlan nonsplitting bases

S. Barry Cooper; Angsheng Li; Xiaoding Yi

doi:10.1007/s001530100095

On the distribution of Lachlan nonsplitting bases

S. Barry Cooper^*
, Angsheng Li
, Xiaoding Yi

^*Corresponding author for this work

University of Leeds
CAS - Institute of Software
University of British Columbia

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 > b, and for any c.e. degrees w, v ≤ a, if a ≤ w ∨ v ∨ b then either a ≤ w ∨ b or a ≤ v ∨ 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.

Original language	English
Pages (from-to)	455-482
Number of pages	28
Journal	Archive for Mathematical Logic
Volume	41
Issue number	5
DOIs	https://doi.org/10.1007/s001530100095
State	Published - Jul 2002
Externally published	Yes

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abstract = "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 > b, and for any c.e. degrees w, v ≤ a, if a ≤ w ∨ v ∨ b then either a ≤ w ∨ b or a ≤ v ∨ 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.",

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AB - 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 > b, and for any c.e. degrees w, v ≤ a, if a ≤ w ∨ v ∨ b then either a ≤ w ∨ b or a ≤ v ∨ 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.

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On the distribution of Lachlan nonsplitting bases

Abstract

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