Direct limits of finite spaces of orderings

Mieczysław Kula, Murray Angus Marshall and Andrzej Sładek

Vol. 112 (1984), No. 2, 391–406

DOI: 10.2140/pjm.1984.112.391

Abstract

Spaces of orderings which are direct limits of finite spaces of orderings arise in a natural way. Every space of orderings is canonically a quotient space of such a space. In this paper we examine the internal structure of such spaces. In particular, we examine how the classification theory for finite spaces of orderings carries over to such spaces. We also establish a relationship between spaces of orderings which are direct limits of finite spaces and certain corresponding types of ultrasums of spaces of orderings. This has application to the problem of representing a space of orderings as the space of orderings of a Pythagorean field.

Mathematical Subject Classification 2000

Primary: 11E04

Secondary: 11E81, 12D15

Milestones

Received: 14 October 1981

Revised: 9 May 1983

Published: 1 June 1984