Office: Room 3312, Mathematics Building
Office Phone: (301) 405-5336
Departmental Fax: (301) 314-0827
E-mail: mcl "at" math.umd.edu
Math 446, Set Theory MWF 1:00-1:50.
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
Non-locally modular types in classifiable theories, with E. Bouscaren, B. Hart and E. Hrushovski, Journal of Mathematical Logic (submitted). .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
When does aleph1-categoricity imply omega-stability? with J. Baldwin and S. Shelah, Model Theory (to appear).
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
Most(?) first order theories have Borel complete reducts, with D. Ulrich, Journal of Symbolic Logic 88 (2023), no. 1, 418-426. .pdf
Characterizing the existence of a Borel complete expansion, with D. Ulrich, Fundamenta Mathematicae 262 (2023) no. 1, 1-35. .pdf
Borel complexity of modules, with D. Ulrich, Annals of Mathematics (submitted) .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
Mutual algebraicity and cellularity, with S. Braunfeld, Archive for Math Logic 61 (2022), no. 5-6, 841-857. .pdf
Theories with few non-algebraic types over models, and their decompositions, with S. Braunfeld, Proceedings AMS 150 (2022), no. 9, 4021-4026. .pdf
Jumps in speeds of hereditary properties in finite relational languages, with C. Terry, Journal of Combinatorial Theory, Series B 154 (2022), 93-135. .pdf
Weakly minimal groups with a new predicate, with G. Conant, Journal of Mathematical Logic 20 (2020), no. 2, 27 pp. .pdf
Counting siblings in universal theories, with S. Braunfeld, Journal of Symbolic Logic 87 (2022), no. 3, 1130-1155. .pdf
Characterizations of monadic NIP, with S. Braunfeld, Transactions of AMS, Series B, 8 (2021), 948-970. .pdf
Worst case expansions of complete theories, with S. Braunfeld, Model theory, 1 no. 1 (2022), 15-30. .pdf
Existential characterizations of monadic NIP, with S. Braunfeld, Communications of AMS (submitted).
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, 1855789 and 2154101.