Mathematical Sciences: Butler Groups of Infinite Rank

点击翻译按钮获取中文摘要

This research is concerned with infinite abelian groups. In particular, it will focus on a collection of torsion-free abelian groups called Butler groups. The principal investigator will investigate the construction and the structure of these groups by using set theoretic methods. This research is in the general area of abelian group theory. The current trend in abelian groups is to utilize set theory and logic in determining questions on structure. Mathematical logic enters into this context since scholars in this subject have discovered that certain research problems in this area are either undecidable in ordinary set theory or else require further set-theoretic axioms for their resolution. This project will concentrate on a subclass of abelian groups called Butler groups.