Singular Coverings and Non-Uniform Notions of Closed Set Computability

Authors:
Stéphane Le Roux;Martin Ziegler
Affiliations:
Japan Advanced Institute of Science and Technology (JAIST) and Ecole normale supérieure de Lyon;Japan Advanced Institute of Science and Technology (JAIST) and University of Paderborn
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

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Abstract

The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe have asserted the existence of non-empty co-r.e. closed sets devoid of computable points: sets which are even 'large' in the sense of positive Lebesgue measure. This leads us to investigate for various classes of computable real subsets whether they always contain a (not necessarily effectively findable) computable point.