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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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