Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 24 / 2 / a / iii

A cofinal map $f:\delta \to \alpha$ has a range cofinal in $\alpha$:For a limit $\alpha$, this is equivalent to $\sup f[\delta ]=\alpha$. For a successor $\alpha$, its largest element must occur in the range. Monotonicity is an additional property and is not part of this definition. The cofinality of $\alpha$ is the least ordinal that admits such a cofinal map into $\alpha$.