This research is concerned with a unified approach to classification problems for torsion, torsion-free, and mixed abelian groups. The principal investigator will continue studying Axiom 3 and equivalence theorems in an effort to access the torsion-free and mixed cases. He is also experimenting with refined concepts of purity to make techniques originally aimed at specific classes of abelian groups more universally useful. This project is in the general area of abelian group theory and is concerned with the classification of abelian groups. Although the classification of finite abelian groups has been well understood for a century, the classification of infinite abelian groups remains elusive. This research involves this old problem of classification of the infinite abelian groups approached by new tools from logic and analysis.
