Abstract: 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).
Keywords: cardinal invariants of the continuum; matrix forcing
DOI: DOI 10.14712/1213-7243.2024.001
AMS Subject Classification: 03E15