Large Countable Ordinals (Part 3)

Last time we saw why it’s devilishly hard to give names to large countable ordinals.

An obvious strategy is to make up a function from ordinals to ordinals that grows really fast, so that is a lot bigger than the ordinal indexing it. This is indeed a good idea. But something funny tends to happen! Eventually catches up with In other words, you eventually hit a solution of

This is called a fixed point of At this point, there’s no way to use as a name for unless you already have a name...