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math.LO2013
Propagation of partial randomness
Kojiro Higuchi, W. M. Phillip Hudelson, Stephen G. Simpson +1
Let f be a computable function from finite sequences of 0's and 1's to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also…
math.LO2013
Harrington's results on arithmetical singletons
Stephen G. Simpson
We exposit two previously unpublished theorems of Leo Harrington. The first theorem says that there exist arithmetical singletons which are arithmetically incomparable. The second…