 of all infinite cardinals numbers ℵα, where α = 0,1,2,… &lt; κ. The ordinals α less than κ form a set (indeed: κ itself). ℵα, better thought of as ℵ(α), is the α-th infinite cardinal number. So ℵ is a function with domain κ, whose value on α is the α-th infinite cardinal number. By Replacement, the set {ℵα | α &lt; κ} exists. Such a set resides at a rank way above κ. 