Varieties of strictly n-generated Heyting algebras

2023/06/21 by Tapani Hyttinen, Hyttinen, Tapani, Davide Emilio Quadrellaro +1
Computer Science · #03C05 #06D20 #08B99 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2306.12250

openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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].

Related

• On locally finite varieties of Heyting algebras
• A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras
• Profiniteness and representability of spectra of Heyting algebras
• Model-completion of varieties of co-Heyting algebras
• Injectives in the variety generated by a finite subdirectly irreducible\n Heyting algebra with involution