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THE TURING DEGREES BELOW GENERICS AND RANDOMS

Published online by Cambridge University Press:  17 April 2014

RICHARD A. SHORE
RICHARD A. SHORE*
Affiliation:
DEPARTMENT OF MATHEMATICS, CORNELL UNIVERSITY, ITHACA NY 14853, USA E-mail: shore@math.cornell.edu
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Abstract

If X0 and X1 are both generic, the theories of the degreesbelow X0 and X1 are the same. The same is true if both arerandom. We show that the n-genericity orn-randomness of X do not suffice to guarantee that the degreesbelow X have these common theories. We also show that these two theories (forgenerics and randoms) are different. These results answer questions of Jockuschas well as Barmpalias, Day and Lewis.

Keywords

Turing degreesn-genericsn-randoms

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 1 , March 2014 , pp. 171 - 178
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

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