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- W33141172 abstract "A real α is computable if its left cut, L(α), is computable. If (qi)i is a computable sequence of rationals computably converging to α, then {qi}, the corresponding set, is always computable. A computably enumerable (c.e.) real α is a real which is the limit of an increasing computable sequence of rationals. It has a left cut which is c.e. We study the Turing degrees of representations of c.e. reals, that is the degrees of increasing computable sequences converging to α. For example, every representation A of α is Turing reducible to L(α). Every noncomputable c.e. real has both a computable representation and a noncomputable representation of degree degTL(α). In fact, the representations of any noncomputable c.e. real are downwards dense, and yet not every c.e. Turing degree below degTL(α) necessarily contains a representation of α." @default.
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- W33141172 date "1999-06-17" @default.
- W33141172 modified "2023-10-17" @default.
- W33141172 title "Degree-Theoretic Aspects of Computably Enumerable Reals" @default.
- W33141172 doi "https://doi.org/10.1017/cbo9780511565670.003" @default.
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