Abstract
We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval (\(\mathrm {BE}\)) is equivalent to weak König lemma (\(\mathrm {WKL}\)) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \(\mathrm {WKL}\) for convex trees, in the framework of constructive reverse mathematics.
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Berger, J., Ishihara, H., Kihara, T. et al. The binary expansion and the intermediate value theorem in constructive reverse mathematics. Arch. Math. Logic 58, 203–217 (2019). https://doi.org/10.1007/s00153-018-0627-2
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DOI: https://doi.org/10.1007/s00153-018-0627-2
Keywords
- The binary expansion
- The intermediate value theorem
- The weak König lemma
- Convex tree
- Constructive reverse mathematics