User blog comment:Googleaarex/Tetrational Arrays/@comment-1605058-20130310210748/@comment-5529393-20130312004352

Just based on Bowers' web page, the strongest notation he has specifically defined is Extended array notation, which has entries below omega^omega. Everything after that is just hinted at through examples and such. However, we have a pretty good idea how tetrational arrays should work:  it's just nested arrays. Chris Bird defines this formally in his Nested Array Notation, which you can find on his web page at Mrob's web site.