4 problems

For every cardinal $\kappa$, let $\mathsf{A}_\kappa$ be the Heyting algebra whose lattice reduct is obtained by adding a new maximum $1$ to the powerset lattice…

Crisp-frame characterization conjecture. The principle $--\Diamond x \rightharpoonup \Diamond --x=\top$ characterizes crisp frames.

Consider formulas of the form … where $I$ is an index set and the $a_i,b_i$ are elements of a Heyting algebra. Closure-ordinal growth conjecture. The closure ordinals of these form…

Let $\mathfrak{A}$ and $\mathfrak{B}$ be Heyting algebras such that $\mathfrak{A}\preccurlyeq\mathfrak{B}$. Let $a\in|\mathfrak{A}|$, and let $(a,a^{\ast})$ be an $\mathcal{E}$-pai…