The binary expansion and the intermediate value theorem in constructive reverse mathematics

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Archive for Mathematical Logic 58 (1-2):203-217 (2019)
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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.

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10.1007/s00153-018-0627-2

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References found in this work

Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Constructive Analysis.Errett Bishop & Douglas Bridges - 1987 - Journal of Symbolic Logic 52 (4):1047-1048.
Foundations of Constructive Analysis.Errett Bishop - 1967 - New York, NY, USA: Mcgraw-Hill.

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