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It is consistent that the continuum be arbitrary large, there is a forcingextension in which no absolute $\kappa$-Borel set $X$ of density $\kappa$,$\aleph_1<\kappa<\mathfrak{c}$, condenses onto a compact metric space. It isconsistent that the continuum be arbitrary large, there is a forcing extensionin which any absolute $\kappa$-Borel set $X$ of density $\kappa$,$\kappa\leq\mathfrak{c}$, containing a closed subspace of the Baire space ofweight $\kappa$, condenses onto a compactum. In particular, applying Brian'sresults 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 whichevery absolute $\aleph_n$-Borel set, containing a closed subspace of the Bairespace of weight $\aleph_n$, condenses onto a compactum if, and only if, $n\inA$.

On the Banach Problem 1 of condensations of absolute $\kappa$-Borel sets onto compacta