Finite models for laws in two variables
Amaryllis Austin · Proceedings of the American Mathematical Society · 1966
The object of this paper is to show that any law involving only two variables, at least one of which occurs on both sides of the law, and w-ary operators, w>0, has a finite model.A law [l, p. 439] is an equation in variables and finitary operators, e.g. the associative law.A model is an algebraic system with finitary operators, i.e. a universal algebra [2, p. 94].By finite model we mean a nontrivial finite model i.e. of order at least two.§ §1 and 2 show how this result is obtained for a single binary operator.In §3 the general result is obtained and also examples are given showing that the result is not true for laws involving nullary operators or more than two variables.