There is a proper countable support iteration of length ω adding no new reals at finite stages and adding a Sacks real in the limit.

In the constructible universe, we construct a co-analytic maximal family of pairwise eventually different functions from $\mathbb{N}$ to which remains after adding arbitrarily many Sacks reals (by countably supported iteration or product).

We consider a property stronger than the Sacks property which holds between the ground model and the Sacks forcing extension. 1. The Shrink Wrapping Property Suppose that V is a Sacks forcing extension of a model M . Then the Sacks property holds between V and M . That is, for each x ∈ ω, there exists a tree T ⊆ ω in M such that x ∈ [T ] and each level of T is finite. The following is a stronge...