Crossref Citations
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Barmpalias, George
and
Lewis-Pye, Andy
2015.
Turing’s Revolution.
p.
207.
Published online by Cambridge University Press: 17 April 2014
If X0 and X1 are both generic, the theories of the degrees below X0 and X1 are the same. The same is true if both are random. We show that the n-genericity or n-randomness of X do not suffice to guarantee that the degrees below X have these common theories. We also show that these two theories (for generics and randoms) are different. These results answer questions of Jockusch as well as Barmpalias, Day and Lewis.