Archive for Mathematical Logic

, Volume 58, Issue 1–2, pp 203–217 | Cite as

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

  • Josef Berger
  • Hajime IshiharaEmail author
  • Takayuki Kihara
  • Takako Nemoto


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.


The binary expansion The intermediate value theorem The weak König lemma Convex tree Constructive reverse mathematics 

Mathematics Subject Classification

03F65 03B30 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Josef Berger
    • 1
  • Hajime Ishihara
    • 2
    Email author
  • Takayuki Kihara
    • 3
  • Takako Nemoto
    • 2
  1. 1.Mathematisches Institut der Universität MünchenMunichGermany
  2. 2.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan
  3. 3.Department of Mathematical Informatics, Graduate School of InformaticsNagoya UniversityNagoyaJapan

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