Submission date: 21 June 2023

Abstract:

For any n <ω we construct an infinite Heyting algebra H_n which is (n+1)-generated but that contains only finite n-generated subalgebras. From this we conclude that for every n < ω there exists a variety of Heyting algebras which contains an infinite (n+1)-generated Heyting algebra, but which contains only finite n-generated Heyting algebras. For the case n=2 this provides a negative answer to a question posed by G. Bezhanishvili and R. Grigolia in [3].

Mathematics Subject Classification: 03C05, 06D20, 08B99

Keywords and phrases:

Full text arXiv 2306.12250: pdf, ps.