Cauchy completeness in elementary logic

Remarks on completeness of lattice-valued Cauchy spaces

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.

On the Cauchy Completeness of the Constructive Cauchy Reals

Intuitionistic set theory without choice axioms does not prove that every Cauchy sequence of rationals has a modulus of convergence, or that the set of Cauchy sequences of rationals is Cauchy complete. Several other related non-provability results are also shown.

A note on Cauchy completeness for preorders

In this paper, we study the notion of Cauchy-complete preorder in a regular category, following work in [CS86], introducing the logic of a regular category. We give a different, stronger characterization than in loc.cit. for those preorders. Using this, we provide a new construction of the Cauchy-completion in a exact category. AMS Classification: 18A40, 03G30.

Change of Base, Cauchy Completeness and Reversibility

We investigate the effect on Cauchy complete objects of the change of base 2-functor V-Cat → W-Cat induced by a two-sided enrichment V → W. We restrict our study to the case of locally partially ordered bases. The reversibility notion introduced in [Wal82] is extended to two-sided enrichments and Cauchy completion. We show that a reversible left adjoint two-sided enrichment F : V → W between lo...

Completeness in modal logic