Vol. 63, No. 2, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
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