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, T/Th 12:30--1:45.
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
A strong failure of aleph_0-stability for atomic classes, with S. Shelah, Archive of Math Logic 58 (2019), Issue 1-2, 99-118. .pdf
Henkin constructions of models with size continuum, with J. Baldwin, Bulletin of Symbolic Logic 25 (2019) 1-33. .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 239 (2017), no. 2, 101-147. .pdf
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
Uniformly bounded arrays and mutually algebraic structures, with C. Terry, Notre Dame Journal of Formal Logic 61 (2020), no. 2, 265-282. .pdf
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, 1308546, and 1855789.