In this paper we study the question assuming MA+⌝CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals 0. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.

We prove that the Sacks forcing collapses the continuum onto ${\frak d}$ , answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses $\omega_2$ then it forces $\diamondsuit_{\omega_{1}}$.