• Corpus ID: 233394496

Pathwise-random trees and models of second-order arithmetic

  title={Pathwise-random trees and models of second-order arithmetic},
  author={George Barmpalias and Weiqi Wang},
. A tree is pathwise-random if all of its paths are algorithmically random. We show that: (a) an algorithmically random real computes a perfect pathwise-random tree if and only if it computes the halting problem; it follows that the class of perfect pathwise-random trees is null, with respect to any computable measure; (b) there exists a positive-measure pathwise-random tree which does not compute any complete extension of Peano arithmetic; and (c) there exists a perfect pathwise-random tree… 
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