Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 24 / 3 / a / i

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- Solution i

Solution

The diagonal intersection of the family is

△_{α < δ} C_{α} = {β < δ : \forall α < β (β \in C_{α})} .

Membership at

β

only tests the sets indexed below

β

, rather than every set of the family. At a regular uncountable

δ

, a diagonal intersection of club sets is again a club set.

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