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

@inproceedings{Willard1999ResiduallyFC,
  title={Residually finite, congruence meet-semidistributive varieties of finite type have a finite residual bound},
  author={R. Willard and K. Kearnes},
  year={1999}
}
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. 
A finite basis theorem for residually finite, congruence meet-semidistributive varieties
  • R. Willard
  • Mathematics, Computer Science
  • Journal of Symbolic Logic
  • 2000
TLDR
A Mal'cev condition for congruence meet-semidistributivity is derived and used to prove two theorems: if a variety in a finite language is congruent and residually less than some finite cardinal, then it is finitely based. Expand
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In this paper we examine four-element and five-element digraphs for existence of certain polymorphisms that imply congruence meet-semidistributivity in a locally finite variety. The results presentedExpand
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Abstract.Weak congruence lattices and semidistributive congruence lattices are both recent topics in universal algebra. This motivates the main result of the present paper, which asserts that aExpand
ON OPTIMAL STRONGMAL ’ CEV CONDITIONS FOR CONGRUENCE MEET – SEMIDISTRIBUTIVITY IN A LOCALLY FINITE VARIETY
In this paper we examine four–element and five–element digraphs for existence of certain polymorphisms that imply congruence meet–semidistributivity in a locally finite variety. The results presentedExpand
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References

SHOWING 1-10 OF 22 REFERENCES
A finite basis theorem for residually finite, congruence meet-semidistributive varieties
  • R. Willard
  • Mathematics, Computer Science
  • Journal of Symbolic Logic
  • 2000
TLDR
A Mal'cev condition for congruence meet-semidistributivity is derived and used to prove two theorems: if a variety in a finite language is congruent and residually less than some finite cardinal, then it is finitely based. Expand
The Residual Bounds of Finite Algebras
  • R. McKenzie
  • Mathematics, Computer Science
  • Int. J. Algebra Comput.
  • 1996
TLDR
An eight-element simple algebra with eight operations that is inherently non-finitely-based and generates a precisely residually countable variety. Expand
Finite equational bases for finite algebras in a congruence-distributive equational class*
Abstract Does every finite algebraic system A with finitely many operations possess a finite list of polynomial identities (laws), valid in A , from which all other such identities follow?Expand
A characterization of varieties with a difference term
We provide more characterizations of varieties with a weak difference term and of neutral varieties. We prove that a variety has a (weak) difference term (is neutral) with respect to theExpand
Affine complete varieties
For an algebra A = (A; F) and a congruence relation 0 of A, a (total) function f i n Ak--*A, (k e w), is compatible with 0 if for all (x 1 . . . . . xk), (y.~, . . . yk) c A ~, xiOy i for i = 1, . .Expand
Semi-categorical algebras. II
Model Theory, Encyclopedia of Mathematics and its Applications 42
  • Model Theory, Encyclopedia of Mathematics and its Applications 42
  • 1993
Model theory
  • W. Hodges
  • Computer Science
  • Encyclopedia of mathematics and its applications
  • 1993
The Structure of Finite Algebras, Contemporary Mathematics 76
  • The Structure of Finite Algebras, Contemporary Mathematics 76
  • 1988
The structure of finite algebras
...
1
2
3
...