I came across the two following Qs in 1970.
Find reals $a,b$ such that $a$ is Sacks over $L[b]$ and vice versa $b$ is Sacks over $L[a]$. Note that a Sacks $\times$ Sacks generic pair definitely does not work.
Suppose that $a$ is Cohen over $L$ and $b$ is Sacks over $L[a]$. Does $a$ belong to $L[b]$? Comment: this Q answers in the positive if $a$ is Sacks or Solovay-random over $L$.
The next Q is perhaps not that dead lock, but still I have no clue.
- Let $\mathbf P$ consist of all perfect sets $P$ on the real plane $\mathbb R\times\mathbb R$ such that all vertical and all horisontal cross-sections of $P$ are perfect (in particular, non-countable). What does it force?