Separating cardinal characteristics of the strong measure zero ideal

Let [Formula: see text] be the [Formula: see text]-ideal of the strong measure zero sets of reals. We present general properties of forcing notions that allow to control of the additivity of [Formula: see text] after finite support iterations. This is applied to force that the four cardinal characteristics associated with [Formula: see text] are pairwise different: [Formula: see text] Furthermore, we construct a forcing extension satisfying the above and Cichoń’s maximum (i.e. that the non-dependent values in Cichoń’s diagram are pairwise different).