On the Cauchy Completeness of the Constructive Cauchy Reals

Robert Lubarsky

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arXiv · 1510.00639

On the Cauchy Completeness of the Constructive Cauchy Reals

Robert Lubarsky

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Abstract

It is consistent with constructive set theory (without Countable Choice, clearly) that the Cauchy reals (equivalence classes of Cauchy sequences of rationals) are not Cauchy complete. Related results are also shown, such as that a Cauchy sequence of rationals may not have a modulus of convergence, and that a Cauchy sequence of Cauchy sequences may not converge to a Cauchy sequence, among others.

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BibTeX RIS

Robert Lubarsky. 2015-10-02. On the Cauchy Completeness of the Constructive Cauchy Reals. https://arxiv.org/abs/1510.00639

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