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Division rings whose vector spaces are pseudofinite
Published online by Cambridge University Press: 12 March 2014
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.
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- Copyright © Association for Symbolic Logic 2010