STRICTLY n-FINITE VARIETIES OF HEYTING ALGEBRAS

Abstract

Abstract For any $n<\omega $ we construct an infinite $(n+1)$ -generated Heyting algebra whose n -generated subalgebras are of cardinality $\leq m_n$ for some positive integer $m_n$ . From this we conclude that for every $n<\omega $ there exists a variety of Heyting algebras which contains an infinite $(n+1)$ -generated algebra, but which contains only finite n -generated algebras. For the case $n=2$ this provides a negative answer to a question posed by G. Bezhanishvili and R. Grigolia in [4].