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The binary expansion and the intermediate value theorem in constructive reverse mathematics
Archive for Mathematical Logic 58 (1-2):203-217 (2019)
Abstract
We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ) is equivalent to weak König lemma ) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \ for convex trees, in the framework of constructive reverse mathematics.Other Versions
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Citations of this work
König's lemma, weak König's lemma, and the decidable fan theorem.Makoto Fujiwara - 2021 - Mathematical Logic Quarterly 67 (2):241-257.
Coding of real‐valued continuous functions under WKL$\mathsf {WKL}$.Tatsuji Kawai - 2023 - Mathematical Logic Quarterly 69 (3):370-391.
References found in this work
Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.
Metamathematical investigation of intuitionistic arithmetic and analysis.Anne S. Troelstra - 1973 - New York,: Springer.
Constructive Analysis.Errett Bishop & Douglas Bridges - 1987 - Journal of Symbolic Logic 52 (4):1047-1048.
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