Strong tree properties for small cardinals
Résumé
Abstract An inaccessible cardinal κ is supercompact when ( κ, λ )-ITP holds for all λ ≥ κ . We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where for every n ≥ 2 and μ ≥ ℕ n , we have (ℕ n , μ )-ITP.