 Solution

ID: past-exam-of-the-analytic-topology-and-axiomatic-set-theory-course-of-the-university-of-oxford/2007/b/5/ii/d/solution

Every set is a subset of itself, so

V_{α} \subseteq V_{α}

. By the successor definition,

V_{α} \in P (V_{α}) = V_{α + 1} .

Membership and inclusion are different statements here; this argument establishes membership of the whole level in its successor.

 New to topics? Read the docs here!