Article
Asymptotic density and the Ershov hierarchy
Mathematical Logic Quarterly
Document Type
Article
Disciplines
Publication Version
Submitted Manuscript
Publication Date
5-1-2015
DOI
10.1002/malq.201300081
Abstract
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.
Copyright Owner
Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Copyright Date
2015
Language
en
File Format
application/pdf
Citation Information
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 Available at: http://works.bepress.com/timothy-mcnicholl/14/
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.