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1 results

  • THE TURING DEGREES BELOW GENERICS AND RANDOMS

  • RICHARD A. SHORE
  • Journal:
    The Journal of Symbolic Logic / Volume 79 / Issue 1 / March 2014
    Published online by Cambridge University Press:
    17 April 2014, pp. 171-178
    Print publication:
    March 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.