# On the distribution of Lachlan nonsplitting bases

@article{Cooper2002OnTD, title={On the distribution of Lachlan nonsplitting bases}, author={S. Barry Cooper and Angsheng Li and Xiaoding Yi}, journal={Archive for Mathematical Logic}, year={2002}, volume={41}, pages={455-482} }

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 or; v or; b then either a ≤ w or; b or a ≤ 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.

## 7 Citations

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### Lachlan Non-Splitting Pairs and High Computably Enumerable Turing Degrees

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Richard Elwes School of Mathematics, University of Leeds, Leeds, LS2 9JT, England R.H.Elwes@leeds.ac.uk Andy Lewis-Pye Department of Mathematics, Columbia House, London School of Economics, Houghton…

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