Null-additive sets and the property gamma

A subset X of the real line is null-additive if for each null set Y, the set X+Y is null. Under Martin Axiom, Galvin nad Miller constructed an uncountable null-additive set whose continuous images are also null-additive; this set has the property gamma, a strong combinatorial covering property. Bartoszyński and Recław proved that, assuming p=c, there is a gamma set that is not null additive. The aim of the talk is to construct sets with the above properties, using weaker set-theoretic assumptions. This is a joint work with Tomasz Weiss.