Effective constructions of existentially closed groups

Abstract: Existentially closed groups were introduced in 1951 by group theorists, in analogue with algebraically closed fields. Since then, they have been further studied by Neumann, Macintyre, and Ziegler, who elucidated deep connections with model theory and computability theory. We review some of the literature on existentially closed groups and present new results that further refine these connections. In particular we find a divergence between local and global complexity not visible from a purely algebraic standpoint.

group theorylogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic