Some foundational questions concerning differential algebraic groups (Q1367611)

The author solves some problems posed by \textit{E. R. Kolchin} in the introduction to his book [Differential algebraic groups. Academic Press, Orlando (1985; Zbl 0556.12006)]. The main result (from which the others follow) is the embeddability of any differential algebraic group in an algebraic group. A crucial intermediate result, and one of independent interest, is a generalisation of Weil's theorem on recovering an algebraic group from birational data, to pro-algebraic groups. In the proof he uses methods and ideas from model theory.