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Keywords:
cardinal invariants of the continuum; matrix forcing
cardinal invariants of the continuum; matrix forcing
Summary:
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 paper Ultrafilters with small generating sets by A. Blass and S. Shelah (1989).
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