Lightface Π_3~0-Completeness of Density Sets Under Effective Wadge Reducibility

摘要

Let A is contained in ~ω2 be measurable. The density set DA is the set of Z ∈ ~ω2 such that the local measure of A along Z tends to 1. Suppose that A is a Π_1~0 set with empty interior and the uniform measure of A is a positive computable real. We show that DA is lightface Π_3~0 complete for effective Wadge reductions. This is an algorithmic version of a result in descriptive set theory by Andretta and Camerlo. They show a completeness result for boldface Π_3~0 sets under plain Wadge reductions.