Abstract
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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Carotenuto, G., Nies, A. (2016). Lightface \(\mathop {\varPi }\nolimits _{3}^{0}\)-Completeness of Density Sets Under Effective Wadge Reducibility. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_24
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DOI: https://doi.org/10.1007/978-3-319-40189-8_24
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