Abstract

We investigate the connection between ▵1 3-stability for random and Cohen forcing notions and the measurability and categoricity of the ▵1 3-sets. We show that Shelah's model for ▵1 3-measurability and categoricity satisfies ▵1 3-random-stability while it does not satisfy ▵1 3-Cohen-stability. This gives an example of measure-category asymmetry. We also present a result concerning finite support iterations of Suslin forcing.