Disambiguation page
There are many different types which are called Cauchy real numbers in the literature. These include:
Cauchy real numbers, which is sometimes defined using Cauchy sequences of a dense integral subdomain of the rational numbers.
generalized Cauchy real numbers, which is defined using all Cauchy nets of a dense integral subdomain of the rational numbers in a universe.
modulated Cauchy real numbers and modulated generalized Cauchy real numbers?, where the modulus of convergence is structure rather than mere property
HoTT book real numbers, which is defined as the homotopy initial -Cauchy structure for the positive terms of a dense integral subdomain of the rational numbers , and called the Cauchy real numbers in the HoTT book.