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

Berger, Josef; Ishihara, Hajime; Kihara, Takayuki; Nemoto, Takako (2019): The binary expansion and the intermediate value theorem in constructive reverse mathematics. In: Archive for Mathematical Logic, Vol. 58, No. 1-2: pp. 203-217

Abstract

We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval (BE) is equivalent to weak Konig lemma (WKL) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to WKL for convex trees, in the framework of constructive reverse mathematics.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0933-5846
• Language: English