A finite basis theorem for difference-term varieties with a finite residual bound (Q2787967)

A variety \textbf{V} of algebras is said to have a \textit{finite residual bound} if there is a finite bound on the size of subdirectly irreducible algebras in \textbf{V}. {R. E. Park}'s conjecture [Equational classes of non-associative ordered algebras. Los Angeles, CA: University of California (PhD Thesis) (1976)] says that every finitely generated variety with a finite residual bound is finitely based. The problem is still open but it was established for: congruence distributive varieties by \textit{K. A. Baker} in [``Equational bases for finite algebras'', Notices Amer. Math. Soc. 19, A-44, 691-08-02 (1972); Adv. Math. 24, 207--243 (1977; Zbl 0356.08006)], congruence modular varieties by \textit{R. McKenzie} in [Algebra Univers. 24, No. 3, 224--250 (1987; Zbl 0648.08006)] and congruence \(\wedge\)-semidistributive varieties by \textit{R. Willard} in [J. Symb. Log. 65, No. 1, 187--200 (2000; Zbl 0973.08004)]. The theorems of McKenzie [loc. cit.] and Willard [loc. cit.] are more general than Baker's [loc. cit.] but incomparable to one another. NEWLINENEWLINENEWLINEThis paper provides a common generalization of the two theorems -- it is done for varieties which have a special ternary term called \textit{a difference term} (and are in a finite language and have a finite residual bound). The paper contains an introduction which gives a good background for understanding \textit{finite basis problems}.