The climbing method is a method used by Jonathan Bowers to create spaces larger than X^^X spaces in BEAF[1], and googologists have attempted to use it to define ordinal tetration and higher hyperoperators. It uses an operation called an "infinity barrier" to represent a power-tower of Xs that has a transfinite number of exponents. As of 2022, it hasn't been formalized in terms of set theory. It means that BEAF is ill-defined in that realm for now.
Expected FGH values[]
According to Sbiis Saibian, the expected FGH ordinals for some values are:
- w^^(w+1) ~ epsilon_omega
- w^^(w+2) ~ epsilon_(omega^omega)
- w^^(w+3) ~ epsilon_(omega^omega^omega)
- w^^w2 ~ epsilon_epsilon_0
...