User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-24920136-20160725013617/@comment-24920136-20160725183750

Ahh i see, i had no clue what that R thing meant, but looking at the paragraph you linked indeed it K seems to cap out at e_0 and not w^w as the overview of the members up to w^3 had me believe.