Publications & Pre-Prints

• Quantifier Eliminable Locally Finite Graphs (with Shawn Hedman), submitted to Mathematical Logic Quarterly, May, 2009.
• Locally Finite Homogeneous Graphs (with Shawn Hedman), accepted by Combinatorica, September 2009.
• Length Spectra of Natural Numbers, to appear in International Journal of Number Theory, September 2009, available at www.arxiv.org.
• Sums of Consecutive Integers, the College Mathematics Journal, Vol. 38, NO. 2, March 2007, p.119–123.
• Rank Inequalities in the Theory of Differentially Closed Fields . Proceedings of Logic Colloquium 2003.
• Orderings of Monomial ideals (with Matthias Aschenbrenner). Fund. Math.
• On Lascar Rank and Morley Ranks of definable groups in differentially closed fields, (with Anand Pillay), Journal of Symbolic Logic. Volume 67. Number 3. Sept. 2002.
• On a result of Rosenlicht. May 2000. Communications in Algebra, Vol. 30, issue 12, 2002, p.5933-5939.
• Chains of Differential Subvarieties of an Algebraic Variety. Journal of Algebra 248, 755-764, 2002.
• Some Applications of Ordinal Dimensions to the Theory of Differentially Closed Fields. Journal of Symbolic Logic. (2000), 65, no. 1, pp.347-356.
• Complete Sets in Differentially Closed Fields. Journal of Algebra 224, 454-466 (2000).
• Ordinal Dimensions and Completeness in Differentially Closed Field. Thesis. May 1999.