I should note that I'm not necessarily looking for a formula that is a finite expression in the alphabet $\land,\lor,\Rrightarrow,j,f^*,f_*$. For example, the formulas given in this answer to another question of mine involve a $\bigwedge$ (infinite meet) in the frame, which is fine by me. Do you think that even with such infinite operations it is still impossible to express the preimage nucleus?
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