turkmath.org

A group G is said to be kappa-existentially closed if every system of less than kappa-many equations and inequations with coefficients in G which has a solution in some supergroup of G already has a solution in G. In this talk, we shall first summarize basic properties of kappa-existentially closed groups and then analyze cardinals kappa and lambda for which there exists a kappa-existentially closed group of cardinality lambda. This is joint work with O. H. Kegel and M. Kuzucuoglu.