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Residually finite, congruence meet-semidistributive varieties of finite type
have a finite residual bound


Authors: Keith A. Kearnes and Ross Willard
Journal: Proc. Amer. Math. Soc. 127 (1999), 2841-2850
MSC (1991): Primary 08B26, 08B10
DOI: https://doi.org/10.1090/S0002-9939-99-05097-2
Published electronically: June 17, 1999
MathSciNet review: 1636966
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that a residually finite, congruence meet-semidistributive variety of finite type is residually $< N$ for some finite $N$. This solves Pixley's problem and a special case of the restricted Quackenbush problem.


References [Enhancements On Off] (What's this?)

  • 1. K. Baker, Finite equational bases for finite algebras in a congruence-distributive equational class, Adv. in Math. 24 (1977), 207-243. MR 56:5389
  • 2. G. Czédli, A characterization of congruence semi-distributivity, in Universal Algebra and Lattice Theory (Proc. Conf. Puebla, 1982), Springer Lecture Notes No. 1004, 1983. MR 85g:08006
  • 3. A. Foster and A. Pixley, Semi-categorical algebras. II, Math. Zeit. 85 (1964), 169-184. MR 29:5771
  • 4. D. Hobby and R. McKenzie, The Structure of Finite Algebras, Contemporary Mathematics 76, American Math. Soc. (Providence, RI), 1988. MR 89m:08001
  • 5. W. Hodges, Model Theory, Encyclopedia of Mathematics and its Applications 42, Cambridge University Press, 1993. MR 94e:03002
  • 6. K. Kaarli and A. Pixley, Affine complete varieties, Algebra Universalis 24 (1987), 74-90. MR 88k:08002
  • 7. K. Kearnes and Á. Szendrei, The relationship between two commutators, to appear in Internat. J. Algebra Comput.
  • 8. P. Lipparini, A characterization of varieties with a difference term, II: neutral $=$ meet semidistributive, Canad. Math. Bull. 41 (1998), 318-327. CMP 98:16
  • 9. R. McKenzie, The residual bounds of finite algebras, Internat. J.Algebra Comput. 6 (1996), 1-28. MR 97e:08002a
  • 10. R. W. Quackenbush, Equational classes generated by finite algebras, Algebra Universalis 1 (1971), 265-266. MR 45:3295
  • 11. W. Taylor, Residually small varieties, Algebra Universalis 2 (1972), 33-53. MR 47:3278
  • 12. R. Willard, A finite basis theorem for residually finite congruence meet-semidistributive varieties, to appear in J. Symbolic Logic.

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Additional Information

Keith A. Kearnes
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email: kearnes@louisville.edu

Ross Willard
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: rdwillar@gillian.math.uwaterloo.ca

DOI: https://doi.org/10.1090/S0002-9939-99-05097-2
Keywords: Congruence distributive, semidistributive, residually finite, variety
Received by editor(s): January 6, 1998
Published electronically: June 17, 1999
Additional Notes: The second author gratefully acknowledges the support of the NSERC of Canada.
Communicated by: Lance W. Small
Article copyright: © Copyright 1999 American Mathematical Society

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