Author:
Ishihara Hajime,Yoshida Satoru
Abstract
AbstractWe show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space (ℝ) of test functions is equivalent to the principle BD-ℕ which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.
Publisher
Cambridge University Press (CUP)
Cited by
17 articles.
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1. The Third Trick;Logical Methods in Computer Science;2022-08-09
2. On Brouwer’s continuity principle;Indagationes Mathematicae;2018-12
3. Principles Weaker than BD-N;The Journal of Symbolic Logic;2013-09
4. On the failure of BD-ℕ and BD, and an application to the anti-specker property;The Journal of Symbolic Logic;2013-03
5. The uniform boundedness theorem and a boundedness principle;Annals of Pure and Applied Logic;2012-08