On the cardinality of nonfinitely based functionally complete algebras (Q1866824)

R. Willard has shown the existence of a 3-element functionally complete algebra which is nonfinitely based. By E. Post, there are only finitely many pairwise term-inequivalent functionally complete two-element algebras. It was shown by by authors and Toršić that the number of at least three-element functionally complete algebras is continuum. The authors have partly used the method of Willard to prove that for each integer \(k\geq 4\) there exist infinitely many pairwise term-inequivalent \(k\)-element algebras of finite type which are functionally complete and inherently nonfinitely based.