Splitting and cone avoidance in the D.C.E. degrees |
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| Authors: | S B Cooper and Angsheng Li |
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| Institution: | 1. Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
2. Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK; Institute of Software, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | It is shown that the Cooper splitting theorem for the n-c.e. degrees is not compatible with cone avoidance: For any n > 1,
there exist n-c.e. degree a, c.e. degree b such that 0 < b < a and such that for any n-c.e. degrees x,y, if x ∨ y = a, then
either b ≤ x or b ≤ y. This provides a new type of elementary difference between the classes of c.e. and d.c.e. degrees, implementable
at lower levels of the high/low hierarchy. |
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| Keywords: | Cooper splitting theorem cone avoidance |
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