  The cardinal invariants $ \mathfrak h, \mathfrak b, \mathfrak s$ of $\mathcal
P (\omega)$ are known to satisfy that $\omega_1 \leq \mathfrak h
\leq\min\{\mathfrak b, \mathfrak s\}$. We prove that all inequalities can be
strict. We also introduce a new upper bound for $\mathfrak h$ and show that it
can be less than $\mathfrak s$. The key method is to utilize finite support
matrix iterations of ccc posets following \cite{BlassShelah}.
