Archimedean lattice-ordered fields that are algebraic over their o-subfields

Niels Schwartz

Vol. 89 (1980), No. 1, 189–198

DOI: 10.2140/pjm.1980.89.189

Abstract

Several properties of archimedean lattice-ordered fields which are algebraic over their o-subfield will be shown to be equivalent. Among these properties are the following: Two geometric descriptions of the positive cone. A sufficient condition for an intermediate field of the lattice-ordered field and its o-subfield to be lattice-ordered. A description of the additive structure of the lattice-ordered field. Two statements on the extendibility of lattice orders to total orders. A statement on the extendibility of a given lattice order to a lattice order on a real closure.

Mathematical Subject Classification 2000

Primary: 06F25

Secondary: 12J15

Milestones

Received: 27 October 1978

Revised: 22 June 1979

Published: 1 July 1980