A short introduction to Ordinal Notations

I will give a pseudo-historical account. The account is historical for I will describe some of the principal developments of the subject in the chronological order of occurrence (with one or two time warps). The account is pseudo for several reasons. Some of the historical remarks may not be strictly accurate. I am not an historian, and I haven’t checked all the appropriate primary sources. However, I haven’t tried to deliberately falsify the story. As with most mathematics, some things we can do better now than when they were first developed. Sometimes I take the more recent approach. This is only a short account, so several, perhaps many, topics have been omitted. At this stage these topics can be seen as peripheral, but in a longer account they would have greater prominence. This account is historical not because I want to write a history, but because I find that mode the easiest way to present this particular material. For some other subjects I would not try an historical account, but for this subject it seems to work. It is hard to find a decent overview or true history of this subject. However, I do recommend [6] for a short history (as it then stood).