User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-5150073-20140515153351/@comment-25418284-20140523070604

I beg your pardon, but I don't see how it's ambiguous or ugly. "First" is a synonym for "smallest," as in "first odd-abundant number" and "first uncountable ordinal." The first fixed point of a function would be its smallest fixed point, i.e. the smallest ordinal a so that f(a) = a. To me this is incredibly obvious!