Abstract
We introduce, and show the equivalences among, relativized versions of Brouwer’s fan theorem for detachable bars (FAN), weak König lemma with a uniqueness hypothesis (WKL!), and the longest path lemma with a uniqueness hypothesis (LPL!) in the spirit of constructive reverse mathematics. We prove that a computable version of minimum principle: if f is a real valued computable uniformly continuous function with at most one minimum on {0,1}N, then there exists a computable α in {0,1}N such that \(f(\alpha) = \inf f(\{0,1\}^\mathbf{N})\), is equivalent to some computably relativized version of FAN, WKL! and LPL!.
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Ishihara, H. (2007). Unique Existence and Computability in Constructive Reverse Mathematics. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_38
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DOI: https://doi.org/10.1007/978-3-540-73001-9_38
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