Abstract
A real number x is computable iff it is the limit of an effectively converging computable sequence of rational numbers, and x is left (right) computable iff 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 {Σn, Πn, Δn : n ∈ ℕ} of real numbers. We characterize the classes Σ2, Π2 and Δ2 in various ways and give several interesting examples.
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