Mathematics, Computer Science
Journal or Book Title
Mathematical Logic Quarterly
We classify the asymptotic densities of the Delta(0)(2) sets according to their level in the Ershov hierarchy. In particular, it is shown that for n2, a real r[0,1] is the density of an n-c.e. set if and only if it is a difference of left-Delta(0)(2) reals. Further, we show that the densities of the w-c.e. sets coincide with the densities of the Delta(0)(2) sets, and there are n-c.e. sets whose density is not the density of an n-c.e. set for any n epsilon omega.
Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Downey, Rod; Jockusch, Carl G.; McNicholl, Timothy H.; and Schupp, Paul E., "Asymptotic density and the Ershov hierarchy" (2015). Mathematics Publications. 108.