Relational Algebraic Approach to the Real Numbers: The Least-Upper-Bound Property
Logic
2026-01-14 v4
Abstract
In this paper we continue the investigation of a real number object, i.e., an object representing the real numbers, in categories of relations. Our axiomatization is based on a relation algebraic version of Tarski's axioms of the real numbers. It was already shown that the addition of such an object forms a dense, linear ordered abelian group. In the current paper we will focus on the least-upper-bound property of such an object.
Keywords
Cite
@article{arxiv.2310.01590,
title = {Relational Algebraic Approach to the Real Numbers: The Least-Upper-Bound Property},
author = {Michael Winter},
journal= {arXiv preprint arXiv:2310.01590},
year = {2026}
}