 Solution

ID: past-exam-of-the-analytic-topology-and-axiomatic-set-theory-course-of-the-university-of-oxford/2009/b/6/iii/a/solution

\forall z \in x (z \in y) .

It expresses

x \subseteq y

x, y \in U_{1}

, transitivity puts every member of

x

U_{1}

already, and membership in

y

has the same meaning in both classes. Thus the formula is

Δ_{0}

and is absolute in both directions, in particular upward absolute.

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