I define a homogeneous ℵ2–c.c. proper product forcing for adding many clubs of ω1 with finite conditions. I use this forcing to build models of b(ω1)=ℵ2, together with d(ω1) and 2ℵ0 large and with very strong failures of club guessing at ω1.
- Baumgartner clubs
- Strong failures of club guessing
- Cardinal characteristics for ω1
- Generalizations of Martin’s Axiom