Lightface \(\mathop {\varPi }\nolimits _{3}^{0}\)-Completeness of Density Sets Under Effective Wadge Reducibility

  • Gemma Carotenuto
  • André Nies
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9709)


Let \(\mathcal {A} \subseteq {}^\omega {2}\) be measurable. The density set \(D \mathcal {A}\) is the set of \(Z \in {}^\omega {2}\) such that the local measure of \(\mathcal {A}\) along Z tends to 1. Suppose that \(\mathcal {A}\) is a \(\varPi ^0_{1}\) set with empty interior and the uniform measure of \(\mathcal {A}\) is a positive computable real. We show that \(D \mathcal {A}\) is lightface \(\varPi ^0_3\) complete for effective Wadge reductions. This is an algorithmic version of a result in descriptive set theory by Andretta and Camerlo [1]. They show a completeness result for boldface \(\varPi ^0_3\) sets under plain Wadge reductions.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversita di SalernoFiscianoItaly
  2. 2.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand

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