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Workshop on Ordered Algebraic Structures
March 9-11, 2000
Vanderbilt University
Nashville, TN, USA

Organizers
Constantine Tsinakis, Jorge Martinez

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f-Rings versus Totally Ordered Rings
by
Bernhard Banaschewski
McMaster University

Given that the classical Birkhoff-Pierce Theorem (1956), characterizing the f-rings as the sub-l-rings of products of totally ordered rings, unavoidably requires the Boolean Prime Ideal Theorem for its proof (Feldman-Henriksen 1988), the question arises whether there is any good relationship between totally ordered and f-rings independent of any choice principles. It will be shown that this is indeed the case by representing any commutative f-ring with unit as the l-ring of global elements of a totally ordered ring in a suitable Grothendieck topos.

Date received: February 16, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caed-19.