User blog comment:SuperSpruce/Can someone teach me how Rathjen’s OCF works?/@comment-35470197-20190723090522/@comment-39541634-20190726145022

I'm don't see what "recursiveness" has to do with understanding fundamental sequences, cofinality or Rathjen's OCF. Nonrecursive countable ordinals don't appear in that OCF anyway (as a side note, any limit countable ordinal - recursive or not - has a cofinality of ω).

What's more of a problem, is that SuperSpruce's definition of cofinality seems to imply that all fundamental sequences of an ordinal have the same length. This is not true. The cofinality of an ordinal is the length of the shortest FS of that ordinal. An ordinal can also have longer FS's. It's just that they won't be optimal.