Journal of Symbolic Logic

Division rings whose vector spaces are pseudofinite

Vinicius Cifú Lopes and Lou van den Dries

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.

Article information

J. Symbolic Logic, Volume 75, Issue 3 (2010), 1087-1090.

First available in Project Euclid: 9 July 2010

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Dries, Lou van den; Cifú Lopes, Vinicius. Division rings whose vector spaces are pseudofinite. J. Symbolic Logic 75 (2010), no. 3, 1087--1090. doi:10.2178/jsl/1278682217.

Export citation