The Hurwitz Matrix Equations and Multifour Groups.
The isomorphism relation on countable torsion free abelian groups is non-Borel.
It is demonstrated that an isotype subgroup of a simply presented abelian group can be simply presented without being a separable subgroup. In particular, the conjecture based on a variety of special cases that Warfield groups are absolutely separable is disproved.
We assign to each pair of positive integers and a digraph whose set of vertices is and for which there is a directed edge from to if . We investigate the structure of . In particular, upper bounds are given for the longest cycle in . We find subdigraphs of , called fundamental constituents of , for which all trees attached to cycle vertices are isomorphic.
We study the -theory of sequences of dual groups and give a complete classification of the -elementary classes by finding simple invariants for them. We show that nonstandard models exist.