Tiltan and Superclub

Abstract

We show that one can force superclub with an arbitrarily large value of $\mathrm{cov}(\mathscr{M})$. We prove that the club principle is consistent with an arbitrarily large value of $\mathrm{add}(\mathscr{M})$. We also prove that if $\kappa $ is regular then superclub at $\kappa ^+$ implies $Q(\kappa ^+,\kappa ^+,\kappa ^+)$.

Keywords

• Superclub
• club (tiltan)
• invariants of measure and category
• infinite graphs
• square brackets