Someone said that Dedekind had a "theory of real numbers", and I wonder about the truth level of that statement. He published the well-known construction of real numbers in 1872, partly inspired by earlier ideas, just like how things usually work out. Today it is treated as an aside, certainly in textbooks on real analysis, it might be mentioned and presented in an appendix, just to show that a set of real numbers does exist as a structure in set theory. I have never before seen mention of an entire theory developed by Dedekind, which if it exists would predate Tarski's formal treatment of the theory of the real ordered field, or something less, or not at all? At the time, maybe Dedekind's paper got considered the basis of a theory, but that just faded away?