Asymptotic density and the Ershov hierarchy |
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| Authors: | Rod Downey Carl Jockusch Timothy H McNicholl Paul Schupp |
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| Affiliation: | 1. School of Mathematics, Statistics, and Operations Research, Victoria University, Wellington, New Zealand;2. Department of Mathematics, University of Illinois at Urbana‐Champaign, Urbana, United States of America;3. Department of Mathematics, Iowa State University, Ames, United States of America |
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| Abstract: | We classify the asymptotic densities of the  sets according to their level in the Ershov hierarchy. In particular, it is shown that for  , a real  is the density of an n‐c.e. set if and only if it is a difference of left‐ reals. Further, we show that the densities of the ω‐c.e. sets coincide with the densities of the  sets, and there are ω‐c.e. sets whose density is not the density of an n‐c.e. set for any  . |
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