Is there a model where Dedekind reals and Cauchy reals are different? I'd appreciate if someone can refer me to any related work in case such a model exists.



A Model where Dedekind Reals and Cauchy Reals are Different
In Lubarsky and Rathjen, *[On the Constructive Dedekind Reals](http://math.fau.edu/lubarsky/Dedreals.pdf)*, Proceedings of LFCS '07, Lecture Notes in Computer Science #4514, they construct a model in which the Cauchy reals form a set, but the Dedekind reals are a proper class. Certainly they are different in this case! The model satisfies a modified version of CZF in which the subset collection axiom schema is replaced by the exponentiation axiom.


