Abstract
The structure of the semi lattice of enumeration degrees has been investigated from many aspects. One aspect is the bounding and nonbounding properties of generic degrees. Copestake proved that every 2-generic enumeration degree bounds a minimal pair and conjectured that there exists a 1-generic set that does not bound a minimal pair. In this paper we verify this longstanding conjecture by constructing such a set using an infinite injury priority argument. The construction is explained in detail. It makes use of a priority tree of strategies.
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References
Copestake, K.: 1-genericity in the enumeration degrees. J. Symbolic Logic 53, 878–887 (1988)
Cooper, S.B., Sorbi, A., Li, A., Yang, Y.: Bounding and nonbounding minimal pairs in the enumeration degrees. J. Symbolic Logic (to appear)
Soare, R.I.: Recursively enumerable sets and degrees. Springer, Heidelberg (1987)
Cooper, S.B.: Computability Theory. Chapman & Hall/CRC Mathematics, Boca Raton (2004)
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© 2006 Springer-Verlag Berlin Heidelberg
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Soskova, M.I. (2006). A Generic Set That Does Not Bound a Minimal Pair. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_71
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DOI: https://doi.org/10.1007/11750321_71
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
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