n the study of strong homology Mardesic and Prasolov isolated a certain inverse system of abelian groups A indexed by functions from \omega to \omega.

They showed that if strong homology is additive on a class of spaces containing closed subsets of Euclidean spaces then the higher derived limits lim^n A must vanish for n >0.

They also proved that under the Continuum Hypothesis lim^1 A does not vanish. On the other hand Down, Simon and Vaughan showed that under PFA lim^1 A=0

The question whether lim^n A vanishes higher n has attracted considerable attention recently. First, Bergfalk shows that it was consistent lim^2 A does not vanish.

Later Bergfalk and Lambie-Hanson showed that, assuming modest large cardinal axioms, lim^n A vanishes for all n. The large cardinal assumption was later removed by Bergfalk, Hrusak and Lambie-Hanson. We complete the picture by showing that, for any n>0, it is relatively consistent with ZFC that lim^n A is non zero.