Free‐decomposability in varieties of semi‐Heyting algebras

Abstract

Abstract In this paper we prove that the free algebras in a subvariety \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal V$\end{document} of the variety \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {SH}$\end{document} of semi‐Heyting algebras are directly decomposable if and only if \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal V$\end{document} satisfies the Stone identity.