Imaginaries in pairs of algebraically closed fields
type: Item
instance of: scholarly article
title: Imaginaries in pairs of algebraically closed fields
zbMATH Open document ID: 1115.03034
published in: Annals of Pure and Applied Logic
publication date: 2007-04-18T00:00:00Z
review text: The paper extends previous work of the author on elimination of imaginaries in pairs of structures [\textit{A. Pillay} and \textit{E. Vassiliev}, ``Imaginaries in beautiful pairs'', Ill. J. Math. 48, No. 3, 759--768 (2004; Zbl 1060.03053)]. He proves \textit{geometric} elimination of imaginaries, viz. that imaginaries are interalgebraic with finite tuples from designated sorts (rather than interdefinable). Roughly, in a pair \(F\subset K\) of algebraically closed fields, the designated quotients consist of orbits of the action of the \(F\)-points of an algebraic group on the \(K\)-points of an algebraic variety, over some other algebraic variety.
reviewed by: Luc Bélair
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 12L12
Mathematics Subject Classification ID: 03C45
zbMATH DE Number: 5144413
zbMATH Keywords: algebraically closed fields
zbMATH Keywords: pair
zbMATH Keywords: imaginary
zbMATH Keywords: algebraic group
author: Anand Pillay
MaRDI profile type: Publication
full work available at URL: j.apal.2006.11.002
OpenAlex ID: W2073422248
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DOI: 10.1016/J.APAL.2006.11.002
description: scientific article; zbMATH DE number 5144413