In 1984 S. Shelah obtains the consistency of \(\mathfrak{b} = \omega_1 < \mathfrak{s} = \omega_2\) using a proper forcing notion of size continuum, which adds a real not split by the ground model reals and satisfies the almost \(\omega^\omega\)-bounding property. We obtain a \(\sigma\)-centered suborder of Shelah's poset, which behaves very similarly to the larger forcing notion: it adds a real not split by the ground model reals and preserves the unboundedness of a chosen unbounded, directed family of reals. Thus under an appropriate finite support iteration of length \(\kappa^+\), where kappa is an arbitrary regular uncountable cardinal, we obtain the consistency of \(\mathfrak{b} = \kappa < \mathfrak{s} = \kappa^+\).
The consistency b = kappa < s = kappa^+
09.10.2008 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25