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math.LO2019
Decidable fan theorem and uniform continuity theorem with continuous moduli
Makoto Fujiwara, Tatsuji Kawai
The uniform continuity theorem (UCT) states that every pointwise continuous real-valued function on the unit interval is uniformly continuous. In constructive mathematics, UCT is s…
math.LO2019
Equivalents of the finitary non-deterministic inductive definitions
Ayana Hirata, Hajime Ishihara, Tatsuji Kawai +1
We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of construc…
math.LO2019
Representing definable functions of by neighbourhood functions
Tatsuji Kawai
Brouwer (1927) claimed that every function from the Baire space to natural numbers is induced by a neighbourhood function whose domain admits bar induction. We show that Brouwer's…