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Asymptotic density and the Ershov hierarchy
Mathematical Logic Quarterly
  • Rod Downey, Victoria University
  • Carl G. Jockusch, University of Illinois at Urbana-Champaign
  • Timothy H. McNicholl, Iowa State University
  • Paul E. Schupp, University of Illinois at Urbana-Champaign
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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.

This is the pre-peer reviewed version of the following article: Downey, Rod, Carl Jockusch, Timothy H. McNicholl, and Paul Schupp. "Asymptotic density and the Ershov hierarchy." Mathematical Logic Quarterly 61, no. 3 (2015): 189-195, which has been published in final form at doi:10.1002/malq.201300081. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving. Posted with permission.

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Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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Rod 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
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