Free $T_n$-Heyting algebras

Abstract

${T}_n$-Heyting algebras form a subvariety of Heyting algebras and are characterized by the property that a chain of prime filters in such an algebra has at most $n-1$ elements. We study some basic properties of these algebras and determine the structure and number of elements of the free ${T}_n$-Heyting algebra with a finite number $r$ of free generators, $FT_n(r)$.