An exploration of weak Heyting algebras: Characterization and properties

This paper explores weak Heyting algebras, an extension of complete Heyting algebras, focusing on characterizing this concept and identifying essential properties in terms of implication operators. The main emphasis is on unraveling the defining features and significance of the novel weak Heyting algebras. We further classify these structures within the context of a complete lattice and extend our findings to the Cartesian product. We facilitate comprehensive comparisons among these structures, by contributing to the broader understanding of weak Heyting algebras in mathematical research.