We show that for any class of Boolean algebras with an associative operator, if it contains the complex algebra of $(\mathcal {P}(\mathbb {N}), \cup )$
, its equational theory is undecidable. Equivalently, any associative normal modal logic valid over the frame $(\mathcal {P}(\mathbb {N}), \cup )$
is undecidable. This settles a long-open question on the decidability of hyperboolean modal logic [16], and addresses several related problems.