Office: Room 3312, Mathematics Building
Office Phone: (301) 405-5336
Departmental Fax: (301) 314-0827
E-mail: mcl "at" math.umd.edu
Math 712, Mathematical Logic I
TTh 11:00-12:15 in MTH 2300.
My current research interest is model theory, broadly defined:
Unique decomposition in classifiable theories, with B. Hart and E. Hrushovski, Journal of Symbolic Logic 67 (2002) 61-68. .ps .pdf
Karp complexity and classes with the independence property, with S. Shelah, Annals of Pure and Applied Logic 120(2003), 263--283. .ps .pdf
Decompositions of saturated models of stable theories, with S. Shelah, Fundamenta Mathematicae 191 (2006) 95-124. .pdf
Conference Presentation (5 April, 2008) Omega-stable theories: Do uncountable languages matter?
P-NDOP and P-decompositions of aleph_epsilon saturated models of superstable theories, with S. Shelah, Fundamenta Mathematicae 229 (2015), no. 1, 47-81. .pdf
Borel completeness of some aleph_0 stable theories, with S. Shelah, Fundamenta Mathematicae 229 (2015), no. 1, 1-46. .pdf
Borel completeness and potential canonical Scott sentences, with D. Ulrich and R. Rast, Fundamenta Mathematicae .pdf (to appear).
Model completeness for trivial, uncountably categorical theories of Morley rank one, with A. Dolich and A. Raichev, Archive for Math. Logic 45(2006) 931-945. .pdf
On the computability-theoretic complexity of trivial, strongly minimal models, with B. Khoussainov, S. Lempp, and R. Solomon, Proc. AMS 135(2007), no. 11, 3711-3721. .pdf
The elementary diagram of a trivial, weakly minimal structure is near model complete, Archive for Math. Logic 48(2009), no 1, 15--24. .pdf
Mutually algebraic structures and expansions by predicates, Journal of Symbolic Logic 78 (2013), 185-194. .pdf
Characterizing model completeness among mutually algebraic structures, Notre Dame Journal of Formal Logic 56 (2015), no. 3, 463-470. .pdf
Conference Presentation (Cesme, Turkey, 20 May, 2012) Mutually algebraic structures and `automatic' quantifier elimination
Conference Presentation (Logic Colloquium 2010, Paris, 26 July, 2010) Compression schemes and definability of types in stable and dependent formulas
On VC-minimal theories and variants, with V. Guingona, Archive for Math Logic 52 (2013), no. 7-8, 743-758. .pdf
Definable choice for a class of weakly o-minimal theories, with C. Shaw, Archive for Math Logic 55 (2016), no. 5-6, 735--748 .pdf
Generalized ordinal sums and BL-chains, with Y.V. Shashoua, Algebra Universalis 52(2004), 137-153. .ps .pdf
Provability in product logic, with S. Malekpour, Archive for Math. Logic 46(2007) 365--378. .ps .pdf
Functional evolution within a protein superfamily, with Z. Yi, O. Vitek, M.A. Qasim, W. Lu, M. Ranjbar, J. Li, M. Laskowski, Jr, and C. Bailey-Kellogg, Proteins 63(3), 2006, 697-708. .pdf
(***) The above research was partially supported by NSF research grants DMS-9403701, 9704364, 0071746, 0300080, 0600217, 0901336, and 1308546.