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On the filter of computably enumerable supersets of an r-maximal set

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Abstract.

We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0 3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706-1388, USA. e-mail: lempp@math.wisc.edu and rsolomon@math.wisc.edu, , , , , , US

    Steffen Lempp & D. Reed Solomon

  2. Department of Mathematics, University of Chicago, Chicago, IL 60637-1514, USA. e-mail: nies@math.uchicago.edu, , , , , , US

    André Nies

Authors
  1. Steffen Lempp
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  2. André Nies
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  3. D. Reed Solomon
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Received: 6 November 1999 / Revised version: 10 March 2000 /¶Published online: 18 May 2001

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Lempp, S., Nies, A. & Solomon, D. On the filter of computably enumerable supersets of an r-maximal set. Arch. Math. Logic 40, 415–423 (2001). https://doi.org/10.1007/PL00003846

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  • DOI: https://doi.org/10.1007/PL00003846