On the Cauchy completeness of the constructive Cauchy reals
Robert S. Lubarsky · Mathematical logic quarterly · 2007
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)