Division rings whose vector spaces are pseudofinite

Lou van den Dries, Vinicius Cifú Lopes

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1087-1090
Number of pages4
JournalJournal of Symbolic Logic
Volume75
Issue number3
DOIs
StatePublished - Sep 1 2010

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Division ring or skew field
Vector space
Thompson's Group
Axiomatization
First-order
Ring

ASJC Scopus subject areas

  • Philosophy
  • Logic

Cite this

Division rings whose vector spaces are pseudofinite. / van den Dries, Lou; Lopes, Vinicius Cifú.

In: Journal of Symbolic Logic, Vol. 75, No. 3, 01.09.2010, p. 1087-1090.

Research output: Contribution to journalArticle

van den Dries, Lou ; Lopes, Vinicius Cifú. / Division rings whose vector spaces are pseudofinite. In: Journal of Symbolic Logic. 2010 ; Vol. 75, No. 3. pp. 1087-1090.
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