  It is consistent that the continuum be arbitrary large and no absolute
$\kappa$-Borel set $X$ of density $\kappa$, $\aleph_1<\kappa<\mathfrak{c}$,
condenses onto a compact metric space. It is consistent that the continuum be
arbitrary large and any absolute $\kappa$-Borel set $X$ of density $\kappa$,
$\kappa\leq\mathfrak{c}$, containing a closed subspace of the Baire space of
weight $\kappa$, condenses onto a compactum. In particular, applying Brian's
results in model theory, we get the following unexpected result. Given any
$A\subseteq \mathbb{N}$ with $1\in A$, there is a forcing extension in which
every absolute $\aleph_n$-Borel set, containing a closed subspace of the Baire
space of weight $\aleph_n$, condenses onto a compactum if, and only if, $n\in
A$.
