On profinite spaces of orderings

TL;DR

This paper characterizes the space of orderings of the rational function field Q(x) as an inverse limit of finite spaces and proves the closure of certain spaces under inverse limits, advancing understanding in algebraic ordering theory.

Contribution

It provides an explicit description of the space of orderings of Q(x) and a new proof that spaces satisfying the pp conjecture are closed under inverse limits.

Findings

Space of orderings of Q(x) as inverse limit of finite spaces

New proof of closure of pp conjecture spaces under inverse limits

Insights into the structure and properties of spaces of orderings

Abstract

In this paper we present the following two results: we give an explicit description of the space of orderings of the field Q(x) as an inverse limit of finite spaces of orderings and we provide a new, simple proof of the fact that the class of spaces of orderings for which the pp conjecture holds true is closed under inverse limits. We discuss how these theorems interact with each other, and explain our motivation to look into these problems.