Tiltan and Superclub

Garti, Shimon; Shelah, Saharon

Comptes Rendus. Mathématique, Tome 361 (2023) no. G5, pp. 853-861

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

Nous prouvons que superclub est consistant avec une valeur arbitrairement élevée de $\mathrm{cov}\left(ℳ\right)$. Nous prouvons que trèfle est consistant avec une valeur arbitrairement élevée de $\mathrm{add}\left(ℳ\right)$. Nous prouvons aussi que superclub en ${\kappa }^{+}$ implique $Q({\kappa }^{+},{\kappa }^{+},{\kappa }^{+})$ si $\kappa$ est un cardinal régulier.

Classification : 05C63, 03E02, 03E17
Keywords: Superclub, club (tiltan), invariants of measure and category, infinite graphs, square brackets

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