Tarski's problem about the elementary theory of free groups has a positive solution.
The combinatorial derivation and its inverse mapping
Let G be a group and P G be the Boolean algebra of all subsets of G. A mapping Δ: P G → P G defined by Δ(A) = {g ∈ G: gA ∩ A is infinite} is called the combinatorial derivation. The mapping Δ can be considered as an analogue of the topological derivation d: P X→ P X, A ↦ A d, where X is a topological space and A d is the set of all limit points of A. We study the behaviour of subsets of G under action of Δ and its inverse mapping ∇. For example, we show that if G is infinite and I is an ideal in...
The elementary theory of Abelian groups with m-chains of pure subgroups
The homomorphic images of infinite symmetric groups.
Theorems on groups of finite Morley rank analogous to theorems on finite groups.
Torsion-free constructive nilpotent -groups.
Transitive groupoids
Two Results on Associativity of Composite Operations in Groups