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Ralph McKenzie Website

Short List of Publications

[1] The residual bounds of finite algebras, International Journal of Algebra and Computation 6 (1996), 1-28.

[2] The residual bound of a finite algebra is not computable, International Journal of Algebra and Computation 6 (1996), 29-48.

[3] Tarski’s finite basis problem is undecidable, International Journal of Algebra and Computation 6 (1996), 49-104.

[4] Arithmetic of finite ordered sets: cancellation of exponents, I, Order 16 (1999), 313-333

[5] Arithmetic of finite ordered sets: cancellation of exponents, II, Order 17 (2000), 309-332.

[6] (with P. Markovic) Few subpowers, congruence distributivity, and near-unanimity terms, Algebra Universalis 58 (2008), 119-128.

 [7] (with E. Aichinger, P. Mayr) On the number of algebraic structures, Journal of the European Mathematical Society (2014) 6, 1673-1686. [PDF]

[8] (with P. Markovic, M. Maroti) Finitely related clones and algebras with cube-terms, Order, 29(2) (2012), 345-359. [PDF]

[9] (with K. Kearnes and P. Markovic) Optimal strong Mal’cev conditions for omitting type 1 in locally finite varieties, Algebra Universalis 72 (2014), 91-100. [PDF]

[10] (with A. Kazda and M. Moore) Absorption and directed Jonsson terms, In: Czelakowski, J. (eds) Don Pigozzi on abstract algebraic logic, universal algebra and Computer Science. Outstanding Contributions to Logic, vol. 16, Springer 2018, pp. 203-220. [PDF]

[11] (with J. Jovanovic, P. Markovic, and M. Moore) Optimal strong Mal’cev conditions for congruence meet semidistributivity in locally finite varieties, Algebra Universalis 76 (2016), no. 3, 305-321.

[12] (with R. Freese) Mal’cev families of varieties closed under join or Mal’cev product, Algebra Universalis 77 (2017), no. 1, 29-50. [PDF]

[13] New directions on finite decidability (manuscript) [PDF]

[14] (with R. Freese, G. McNulty, and W. Taylor) Algebras, Lattices, Varieties II, (in progress).

[15] (with M. Moore) Colorings of free algebras, splittings in the lattices of interpretability. (in progress).

[16] (with P. Markovic) On the constraint satisfaction problem for semilattices of Mal’cev blocks (in progress).