{For every regular cardinal $\omega_\mu$, we construct
an $\omega_{\mu}$-Nagata space that is
not $\omega_{\mu}$-metrizable (it does not have an ortho-base), and an
$\omega_\mu$-stratifiable space that is not 
$\omega_\mu$-Nagata.  We prove that every $\om$-Nagata space, for $\om$ uncountable,
is ultraparacompact.  For every set $S$ of
regular cardinals, we construct a space $X(S)$ such that $X(S)$ is stratifiable over every  $\kappa \in
S$, and
$X(S)$ is not stratifiable over any $\kappa \not\in S$ provided there does not exist
 an inaccessible
cardinal.  We show that the countable box product of stratifiable space need not be stratifiable
even if the product is $\om$-stratifiable, hence hereditarily paracompact and monotonically
normal. We construct a space $X$ stratifiable over
$\omega_\mu$ (and not stratifiable over any other regular cardinal) such that  
$\omega=\psi(X)<\omega_\mu<\chi(X)$.