Vol. 89, No. 1, 1980

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

Niels Schwartz

Vol. 89 (1980), No. 1, 189–198

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
Received: 27 October 1978
Revised: 22 June 1979
Published: 1 July 1980
Niels Schwartz