Vol. 63, No. 2, 1976

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Lattice orderings on the real field

Robert Ross Wilson

Vol. 63 (1976), No. 2, 571–577
Abstract

Since every total order is a lattice order, and the real field R is a totally ordered field, it is a lattice-ordered field. In 1956 Birkhoff and Pierce raised the question of whether R can be made into a lattice-ordered field in any other way. In this paper we answer their question affirmatively by showing that there are, in fact, 2c such orderings, where c is the cardinal of R.

Mathematical Subject Classification 2000
Primary: 12D99
Secondary: 12J15
Milestones
Received: 20 August 1974
Revised: 11 June 1975
Published: 1 April 1976
Authors
Robert Ross Wilson