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We demonstrate how most common cardinal invariants associated to a von Neumann algebra M can be computed from the decomposability number, dec(M), and the minimal cardinality of a generating set, gen(M). Applications include the equivalence of the well-known generator problem, "Is every separably-acting von Neumann algebra singly-generated?", with the formally stronger questions, "Is every countably-generated von Neumann algebra singly-generated?" and "Is the gen invariant monotone?" Modulo thedoi:10.4153/cjm-2011-048-2 fatcat:gpehuqbt4nd3tgqfttt6yknnuq