Abstract
A real number is computable if it is the limit of an effectively converging computable sequence of rational numbers, and left (right) computable if it is the supremum (infimum) of a computable sequence of rational numbers. By applying the operations “sup” and “inf” alternately n times to computable (multiple) sequences of rational numbers we introduce a non-collapsing hierarchy Σ n , Π n , Δ n : n ∈ ℕ of real numbers. We characterize the classes Σ 2 Π 2 and Δ 2 in various ways and give several interesting examples.
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Zheng, X., Weihrauch, K. (1999). The Arithmetical Hierarchy of Real Numbers. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_3
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DOI: https://doi.org/10.1007/3-540-48340-3_3
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