Counting the changes of random Δ20 sets

  • Authors:

  • Santiago Figueira;Denis Hirschfeldt;Joseph S. Miller;Keng Meng Ng;André Nies

  • Affiliations:

  • Dept. of Computer Science, FCEyN, University of Buenos Aires and CONICET;Dept. of Mathematics, The University of Chicago;Dept. of Mathematics, University of Wisconsin-Madison;Dept. of Mathematics, University of Wisconsin-Madison;Dept. of Computer Science, The University of Auckland

  • Venue:
  • CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
  • Year:
  • 2010

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Abstract

Consider a Martin-Löf random Δ20 set Z. We give lower bounds for the number of changes of Zs ↑n for computable approximations of Z. We show that each nonempty Π10 class has a low member Z with a computable approximation that changes only o(2n) times. We prove that each superlow ML-random set already satisfies a stronger randomness notion called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that Zs ↑n changes more than c2n times.