 We now return to the proof of the CH in L. We used the Mostowski Collapse to construct the transitive set N. As it turns out, the real number A is still an element of &lt; N, ∈ &gt; . By basic properties of L, &lt; N, ∈ &gt; must be &lt; Lα , ∈ &gt; for some α . Since N is countable, α is countable too. (It can be shown that |Lα| = |α| + ℵ0.) Thus A is constructible on a countable level, which was to have been shown.