User blog:Tetramur/Robert Munafo and extending his PT notation

a PT 1 = 10^^a

a PPT 1 = a PT 1 PT 1 PT 1 PT 1 ... PT 1 with (a-1) PT = 10^^^a

(PT is left-associative)

a PPPT 1 = a P(3)T 1  = 10^^^^a

a P(4)T 1 = {10,a,5}

a P(n)T 1 = {10,a,n+1}

this is limit of extended PT notation and has the limit \(\omega)\ in standard FGH.