Mathematical Logic Quarterly 50 (1):47-50 (2004)

Suppose that 〈xk〉k∈ℕ is a countable sequence of real numbers. Working in the usual subsystems for reverse mathematics, RCA0 suffices to prove the existence of a sequence of reals 〈uk〉k∈ℕ such that for each k, uk is the minimum of {x0, x1, …, xk}. However, if we wish to prove the existence of a sequence of integer indices of minima of initial segments of 〈xk〉k∈ℕ, the stronger subsystem WKL0 is required. Following the presentation of these reverse mathematics results, we will derive computability theoretic corollaries and use them to illustrate a distinction between computable analysis and constructive analysis
Keywords constructive analysis  computable analysis  Reverse mathematics
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DOI 10.1002/malq.200310075
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Reverse Mathematics of Separably Closed Sets.Jeffry L. Hirst - 2006 - Archive for Mathematical Logic 45 (1):1-2.

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