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Division rings whose vector spaces are pseudofinite

Published online by Cambridge University Press:  12 March 2014

Lou van den Dries and
Vinicius Cifú Lopes
Lou van den Dries
Affiliation:
University of Illinois at Urbana-Champaign, 1409 West Green Street Urbana, Il 61801, USA. E-mail: vddries@math.uiuc.edu
Vinicius Cifú Lopes
Affiliation:
University of Illinois at Urbana-Champaign, 1409 West Green Street Urbana, Il 61801, USA. E-mail: vinicius@alumni.illinois.edu
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Abstract

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.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010, pp. 1087 - 1090
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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