  It is well-known that if $Y$ is a Banach space the $weak^{*}$-fragmentability
of its dual space by some metric $\rho$ implies that $Y^{*}$ belongs to the
Stegall class -- the former for shortly $\mathcal{W^*}F$, being the latter
$\mathcal{S}$ and hence $Y$ is weak Asplund -- call it $\mathcal{WA}$ . It has
been proved by O. Kalenda and Kunen that existence of a measurable cardinal
implies (it is consistent) that, for instance in the construction of Kalenda
Compacts - this space is in the Stegall`s class iff both inclusions of classes
are strictly proper. The same authors made following question, is there a model
of ZFC, in which the inclusion of $\mathcal{WA}$ in $\mathcal{S}$ actually is
equality. Obviously, because of their result the existence of large cardinals (
supercompacts, strongly-compacts, strong cardinals, huge cardinals, Vop\v{e}nka
principle) would be a models of the proper inclusion of the above - mentioned
classes, being with more consistency power even, see Thomas Jech [TJ03] and
Saharon Shelah [SSH17].
