Preserving measurability with Cohen iterations

Abstract

We describe a weak version of Laver indestructibility for a μ-tall cardinal κ, μ > κ+, where “weaker” means that the indestructibility refers only to the Cohen forcing at κ of a certain length. A special case of this construction is: if μ is equal to κ+n for some 1 < n < ω, then one can get a model V∗ where κ is measurable, and its measurability is indestructible by Add(κ, α) for any 0 ≤ α ≤ κ+n (Theorem 3.3).

Keywords

• Cohen forcing
• measurability