If x_0 and x_1 are both generic, the theories of the degrees below x_0 and x_1 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.
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