  We prove the following consistency result for cardinal sequences of length $<
\om_3$: if GCH holds and $\la \geq \om_2$ is a regular cardinal, then in some
cardinal-preserving generic extension $2^{\om} = \la$ and for every ordinal
$\eta < \om_3$ and every sequence $f = \langle \ka_{\al} : \al < \eta \rangle$
  of infinite cardinals with $\ka_{\al}\leq \la$ for $\al < \eta$ and
$\ka_{\al} = \om$ if $\mbox{cf}(\al) = \om_2$, we have that $f$ is the cardinal
sequence of some LCS space.
  Also, we prove that for every specific uncountable cardinal $\lambda$ it is
relatively consistent with ZFC that for every $\al,\be < \om_3$ with
$\mbox{cf}(\al) < \om_2$ there is an LCS space $Z$ such that $\mbox{CS}(Z) =
\langle \omega \rangle_{\alpha}\concat \langle \lambda \rangle_{\beta}$.
