Abstract

We prove that if $$\mathcal {A}$$ A is an infinite Boolean algebra in the ground model V and $$\mathbb {P}$$ P is a notion of forcing adding any of the following reals: a Cohen real, an unsplit real, or a random real, then, in any $$\mathbb {P}$$ P -generic extension V[G], $$\mathcal {A}$$ A has neither the Nikodym property nor the Grothendieck property. A similar result is also proved for a dominating real and the Nikodym property.