EDUCATION

A.B., Columbia College, New York, New York, 1964

Ph.D., Cornell University, Ithaca, New York, 1968

RESEARCH AREA

Logic and algebra (Model theory; module theory; applications of model theory and set theory to algebra)

PROFESSIONAL EXPERIENCE

Gibbs Instructor in Mathematics, Yale University, New Haven, Connecticut, 1968-1970

Assistant Professor of Mathematics, Stanford University, Stanford, California, 1970-1973

Associate Professor of Mathematics, University of California, Irvine, 1973-1978

Visiting Associate Professor of Mathematics, Yale University, New Haven, Connecticut, 1975-1976

Visiting Professor of Mathematics, Simon Fraser University, Burnaby, B.C., Jan.- July 1985

Professor of Mathematics, University of California, Irvine, 1978-2007

Professor Emeritus of Mathematics, University of California, Irvine, 2007 -

INVITED LECTURES

• Lecture series, NSF-supported workshop on Set-theoretic methods in algebra, Baylor University, May 1990
• Logic Meeting (MAMLS), Rutgers, September 1990
• Conference on Modules and Commutative Rings, Bressanone, Italy, October 1990
• Conference on Torsion Free Abelian Groups, Cura\c{c}ao, August 1991
• Logic Meeting (MAMLS), Rutgers, Oct. 1992
• Module Theory Conference, Prague, Sept. 1993
• Abelian Groups and Modules Conference, Padova, June 1994
• Logic Meeting (MAMLS), Rutgers, Sept. 1994
• Algebra and Model Theory Conference, Dresden, June 1995
• Abelian groups and Modules Conference, Colorado Springs, August 1995
• Module Theory Conference, Prague, Sept. 1995
• Algebra Conference, Prague, Sept. 1997
• Lecture series, Euroconference “Infinite length modules'', Bielefeld, Germany Sept. 1998
• Lecture series, Euroconference “Infinite combinatorics and their impact on algebra'', Hattigen, Germany, June-July, 1999
• Modules and Abelian Groups Workshop, Brixen, Italy, July 1999.
• Algebra Conference, Prague, Sept. 1999.
• Southern California Algebra Conference, UCLA, May, 2000
• Special Session on Representation Theory of Algebras, Amer. Math. Soc. Regional Meeting, Santa Barbara, March 2000
• Abelian Groups and Modules Conference, Honolulu, July 2001
• Euroconference “Algebra and discrete mathematics'', Hattigen, Germany, August 2001
• “Algebra-Geometry and Interactions'' conference, Hattingen, Germany, July 2002
• Canadian Math Society Symposium on “Model Theory and Recursion Theory'', Vancouver, Dec. 2003
• AMS Regional Meeting Special Section on “Representation Theory of Algebras'', Santa Barbara, Apr. 2004
• MAMLS Conference in honor of the 60th birthday of Saharon Shelah, Rutgers University, Oct. 2005
• Algebra Conference in honor of the 60th birthday of Luigi Salce, Padua, Italy, June 2006: “New results on Whitehead groups” Padua-lecture.pdf
• Second Czech-Catalan Conference in Mathematics, Barcelona, Spain, September 2006: “Set-theoretic methods in module theory” Barcelona-lecture.pdf
• Stanford Logic Seminar, February 2009: “Some uses of set theory in algebra”  stanford.pdf

RECENT PUBLICATIONS

• Baer modules over domains (with L. Fuchs and S. Shelah), Transactions of Amer. Math. Soc., 322 (1990), 547-560.
• Almost Free Modules: Set-theoretic methods, (with A. Mekler), North-Holland Publishing Company (1990), 482 pages.
• On Whitehead Modules (with S. Shelah), J. of Algebra 142 (1991), 492-510.
• A transfer theorem for non-standard uniserials, Proceedings of Amer. Math. Soc. 114 (1992), 593-600.
• Set-theoretic methods: the uses of Gamma invariants, in Abelian Groups, the proceedings of the Curaçao conference on torsion-free abelian groups, Lecture Notes in Pure and Applied Math. No. 146, Marcel Dekker (1993), 143-153.
• On a conjecture regarding non-standard uniserial modules (with S. Shelah), Trans. Amer. Math. Soc., 140 (1993), 337-351.
• Uniformization and the diversity of Whitehead groups (with A. Mekler and S. Shelah), Israel J. Math. 80 (1992), 301-321.
• Explicitly non-standard uniserial modules (with S. Shelah), J. Pure and Applied Algebra, 86 (1993), 35-50.
• Hereditarily separable groups and monochromatic uniformization (with A. Mekler and S. Shelah), Israel J. Math., 88 (1994), 213-235.
• Model theory of modules over a serial ring (with I. Herzog), Annals of Pure and App. Logic 72 (1995), 145-176.
• A combinatorial principle equivalent to the existence of non-free Whitehead groups (with S. Shelah), in Abelian Group Theory and Related Topics, Contemporary Math. v. 171 (1994), 79-98.
• On invariants for w₁-separable groups (with M. Foreman and S. Shelah), Trans. Amer. Math. Soc. 347 (1995), 4385-4402.
• Torsion modules, lattices and p-points (with B. Huisgen-Zimmermann and S. Shelah), Bulletin of London Math. Soc. 29(1997), 547-555.
• Set theory generated by abelian group theory, Bulletin of Symbolic Logic, 3 (1997), 1-16.
• The Kaplansky test problems for N₁-separable groups (with S. Shelah), Proc. Amer Math. Soc. 126(1998), 1901-1907.
• Gamma invariants for dense lattices (with J. Trlifaj), Algebra Universalis, 40 (1998), 427-445.
• Absolutely rigid systems and absolutely indecomposable groups (with S. Shelah),in Abelian Groups and Modules (ed. P. Eklof and R. Goebel), Birkhaeuser (1999), 257-268. Correction
• A non-reflexive Whitehead group (with S. Shelah), J. of Pure and Applied Algebra 156 (2001), 199-214.
• Modules with strange decomposition properties , in Infinite Length Modules (ed. H. Krause and C. M. Ringel), Birkhaeuser, 75-87.
• How to make Ext vanish (with J. Trlifaj), Bull. London Math. Soc. 33 (2001), 41-51.
• Covers induced by Ext (with J. Trlifaj), J. Algebra 231 (2000), 640-651.
• Whitehead modules, invited chapter for Handbook of Algebra (ed. M. Hazewinkel), volume 3 (2003), 317-341 (Elsevier)
• The structure of Ext (A,Z) and GCH: possible co-Moore spaces (with S. Shelah), Math. Zeit. 239 (2002), 143-157.
• Whitehead modules over large principal ideal domains (with S. Shelah), Forum Math. 14 (2002), 477-482.
• The affinity of set theory and abelian group theory , Rocky Mt. J., 32 (2002), 1119--1134.
• Almost Free Modules: Set-theoretic methods, Revised edition , North-Holland Mathematical Library vol. 65 (2002), 597 pages. Errata, Update on open problems
• On the existence of precovers (with S. Shelah), Illinois J. Math. 47(2003), 173-188.
• On the cogeneration of cotorsion pairs (with S. Shelah and J. Trlifaj), J. Algebra 277 (2004), 572--578.
• Tilting cotorsion pairs (with S. Bazzoni and J. Trlifaj), Bull. London Math. Soc. 37 (2005), 683—696..
• Test groups for Whitehead groups (with L. Fuchs and S. Shelah), Rocky Mt. J. Math, to appear.Whtest.pdf
• ^⊥N as an abstract elementary class (with J. Baldwin and J. Trlifaj), Annals of Pure and App. Logic 149 (2007), 25-39, Nperp-aec.pdf
• Shelah's Singular Compactness Theorem, Publicacions Matematiques 52 (2008), 3-18 SingComp.pdf

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