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Degrees bounding minimal degrees

Published online by Cambridge University Press:  24 October 2008

C. T. Chong  and
R. G. Downey
C. T. Chong
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, 0511, Singapore
R. G. Downey
Affiliation:
Department of Mathematics, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand
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Extract

A set is called n-generic if it is Cohen generic for n-quantifier arithmetic. A (Turing) degree is n-generic if it contains an n-generic set. Our interest in this paper is the relationship between n-generic (indeed 1-generic) degrees and minimal degrees, i.e. degrees which are non-recursive and which bound no degrees intermediate between them and the recursive degree. It is known that n-generic degrees and minimal degrees have a complex relationship since Cohen forcing and Sacks forcing are mutually incompatible. The goal of this paper is to show.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 211 - 222
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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