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

Archive for Mathematical Logic 40 (6):415-423 (2001)

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)
Keywords Key words or phrases: Computably enumerable set – r-maximal set – Superset – Tower
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DOI 10.1007/PL00003846
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