Paul C. EklofProfessor Emeritus, Mathematics 

Research Interests 
Model theory, set theory, abelian groups, modules, settheoretic algebra  
URL  math.uci.edu/~peklof/  
Research Abstract 
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, coauthored 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 settheoretic methods to module theory and representation theory.  
Publications  Shelah's singular compactness theorem, Publ. Mat. 52 (2008), 318  
Tilting cotorsion pairs (with S. Bazzoni and J. Trlifaj), Bull. LMS 37 (2005), 683696  
$^\perpN$ as an abstract elementary class (with J. Baldwin and J. Trlijaf), Annals of Pure and Applied Logic (2007)  
Almost Free Modules: Settheoretic methods, Revised Edition, Elsevier Science, (2002), 620 pages. 

(with S. Shelah and J. Trlifaj) On the cogeneration of cotorsion pairs, J. Alg. 277 (2004), 572578.  
(with S. Shelah) On the existence of precovers, Ill. J. Math. 47 (2003), 173188.  
(with S. Shelah) The structure of Ext(A, Z) and GCH: possible coMoore spaces, Math. Zeit. v. 239 (2002), 143157.  
(with J. Trlifaj) How to make Ext vanish, Bull. London Math. Society v.33 (2001), 4151. 

(with J. Trlifaj) Covers induced by Ext, J. Algebra, v. 231(2000), 640651.  
(with S. Shelah)The Kaplansky test problems for \aleph_1  separable groups, Proc. Amer. Math. Soc 126(1998), 19011907. 

Professional Societies 
American Mathematical Society Association for Symbolic Logic 

Link to this profile  http://www.faculty.uci.edu/profile.cfm?faculty_id=2012  
Last updated  12/17/2008  