Let a finite structure be a finite underlying set A along with a finite set of finitary operation from A to itself. Such creatures are called algebras in the study of universal algebra, and one subarea of study is the equational theory of such a creature, i.e. the set of universally quantified equations which hold in the strucure (e.g. the associative law for semigroups).
The equational theory is said to be finitely based if there is a finite set of equations from which one can deduce precisely those equations in the equational theory.

A problem raised by Tarski and shown undecidable by McKenzie is Tarski's Finite Basis Problem: Given a finite structure , determine whether its equational theory is finitely based.

Gerhard "Ask Me About System Design" Paseman, 2010.01.12