How to construct an ordinal with uncountable cofinality? All the very "large" ordinals I can think of, such as $\omega_\omega^{\omega_\omega}$, still seem to have countable cofinality. I need a better intuitive sense of what such a large ordinal can be.
Relevant links: http://en.wikipedia.org/wiki/Cofinality#Cofinality_of_ordinals_and_other_well-ordered_sets http://en.wikipedia.org/wiki/Ordinal_number