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math.LO2026
The strength of the minimum principle in constructive reverse mathematics
Tatsuji Kawai
The minimum principle states that every real-valued uniformly continuous function f : X -> R on a compact metric space X attains its minimum. Working in the base system EL0 of cons…
math.LO2026
Constructive equivalence between Brouwer's fixed-point theorem and weak König's lemma
Tatsuji Kawai
In the context of constructive reverse mathematics, we show that Brouwer's fixed-point theorem and weak König's lemma (WKL) are equivalent. To derive WKL from Brouwer's fixed-point…