 Solution

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

Here

Z F^{*}

V_{0} = \emptyset, V_{α + 1} = P (V_{α}), V_{λ} = β < λ ⋃ V_{β} (λ a nonzero limit) .

The associated class is

V = {x : \exists α \in Ord (x \in V_{α})}

. Each level is a set, while

V

is a definable class. Without Foundation it need not contain every ambient set; it consists of the sets built by this well-founded hierarchy.

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