User blog comment:Wythagoras/All my stuff/@comment-5029411-20131103132246

KAI X~ from FGH Part 2

\(\alpha\)(0,0,1)(n) has growth rate phi(w^2,0)

\(\alpha\)(0...0,1)(n) (m 0's) has growth rate phi(w^m,0)

\(\beta\)(0)(n) has growth rate phi(w^w,0)

\(\beta\)(m)(n) has growth rate phi(phi(m,0),0)

\(\beta\)(0,1)(n) has growth rate phi(phi(w,0),0)

\(\gamma\)(0)(n) has growth rate phi(phi(w^w,0),0)

\(\delta\)(0)(n) has growth rate phi(phi(phi(w^w,0),0),0)

...

\(\omega\)(0)(n) has growth rate phi(...phi(w^w,0)...,0) (24 nested)

X(1) > f_{phi(...phi(75!,0)...,0)}(75!) (25 nested)

X(n) > f_{phi(...phi(X(n-1)!,0)...,0)}(X(n-1)!) (25 nested)

n!m has growth rate m+2

U > f_{f_{...f_{f_2(75)}(75)+2...}(75)+2}(75) (75! nested)

Part 3 Coming Soon!