Model theory, set theory, abelian groups, modules, set-theoretic algebra
Dr. Eklof's research has generally dealt with applications of mathematical logic, specifically model theory and set theory, to algebra, specifically abelian group theory, module theory, and homological algebra. This has included the model theory of modules as well as properties of abelian groups expressible in various extensions of first order logic. In recent years, the main focus has been on algebraic results which are provably unsolvable in ordinary set theory or are solved using methods from combinatorial set theory. A major monograph on this subject, co-authored orignially with the late Alan Mekler, was published in 1990; a revised and expanded edition was published in 2002. His work, with Jan Trlifaj, has provided the key element of a recent proof of a long standing conjecture, the Flat Cover Conjecture and applied set-theoretic methods to module theory and representation theory.
Shelah's singular compactness theorem, Publ. Mat. 52 (2008), 3-18
Tilting cotorsion pairs (with S. Bazzoni and J. Trlifaj), Bull. LMS 37 (2005), 683-696
$^\perpN$ as an abstract elementary class (with J. Baldwin and J. Trlijaf), Annals of Pure and Applied Logic (2007)
Almost Free Modules: Set-theoretic methods, Revised Edition, Elsevier Science, (2002), 620 pages.
(with S. Shelah and J. Trlifaj) On the cogeneration of cotorsion pairs, J. Alg. 277 (2004), 572-578.
(with S. Shelah) On the existence of precovers, Ill. J. Math. 47 (2003), 173-188.
(with S. Shelah) The structure of Ext(A, Z) and GCH: possible co-Moore spaces, Math. Zeit. v. 239 (2002), 143-157.
(with J. Trlifaj) How to make Ext vanish, Bull. London Math. Society v.33 (2001), 41-51.
(with J. Trlifaj) Covers induced by Ext, J. Algebra, v. 231(2000), 640-651.
(with S. Shelah)The Kaplansky test problems for \aleph_1 - separable groups,
Proc. Amer. Math. Soc 126(1998), 1901-1907.
American Mathematical Society
Association for Symbolic Logic