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A constructive look at the completeness of the space (ℝ)

Published online by Cambridge University Press:  12 March 2014

Hajime Ishihara  and
Satoru Yoshida
Hajime Ishihara
Affiliation:
School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan, E-mail: [email protected]
Satoru Yoshida
Affiliation:
School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan, E-mail: [email protected]
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Abstract

We 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1511 - 1519
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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