Asymptotic density and the Ershov hierarchyMathematical Logic Quarterly
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AbstractWe 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.
Copyright OwnerWiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Citation InformationRod Downey, Carl G. Jockusch, Timothy H. McNicholl and Paul E. Schupp. "Asymptotic density and the Ershov hierarchy" Mathematical Logic Quarterly Vol. 61 Iss. 3 (2015) p. 189 - 195
Available at: http://works.bepress.com/timothy-mcnicholl/14/