✦ LIBER ✦

On the Cauchy completeness of the constructive Cauchy reals

✍ Scribed by Robert S. Lubarsky

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 200 KB
Volume: 53
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200710007

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✦ Synopsis

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. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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