Imaginaries in pairs of algebraically closed fields
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.
scientific article; zbMATH DE number 5144413
scientific article