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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: [email protected]
Vinicius Cifú Lopes
Affiliation:
University of Illinois at Urbana-Champaign, 1409 West Green Street Urbana, Il 61801, USA. E-mail: [email protected]
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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.

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

REFERENCES

[1]Blanchard, A., Les corps non commutatifs, Collection SUP: Le Mathématicien, no. 9, Presses Universitaires de France, Vendôme, 1972, 135 pp. in French.Google Scholar
[2]Cannon, J.W., Floyd, W. J., and Parry, W. R., Introductory notes on Richard Thompson's Groups, Enseignement Mathématique. Revue Internationale. Ile Série., vol. 42 (1996), pp. 215–256.Google Scholar
[3]van den Dries, L. and Vinicius, C. L., Invariant measures on groups satisfying various chain conditions, this Journal, to appear.Google Scholar
[4]Fuchs, L., Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris, 1963, Addison-Wesley Publishing Co., Inc., Reading-Palo Alto-London, ix + 229 pp.Google Scholar
[5]Vinicius, C. L., Euler characteristics for strongly minimal groups and the eq-expansions of vector spaces, submitted.Google Scholar