The climbing method is a method used by Jonathan Bowers to create spaces larger than X^^X spaces in BEAF. It uses an operation called an "infinity barrier" to represent a power-tower of Xs that has a transfinite number of exponents. As of July 2020, it hasn't been formalized in terms of set theory. It means that BEAF is ill-defined in that realm for now.
- Jonathan Bowers, Spaces (2020)