Fast Growing Hierarchy Calculator ~repack~ -

Unlocking the Infinite: A Comprehensive Guide to the Fast Growing Hierarchy Calculator

• Fast-growing hierarchies are families of functions (fα) indexed by ordinals α that increase rapidly with α.
• They are used to compare proof-theoretic strength and to classify computable/incomputable growth rates.
• Typical base: choose a base function f0 (often the successor n ↦ n+1 or a linear function) and define fα for successor and limit ordinals using iterations or diagonalization.

def _f(self, alpha, n): self.steps += 1 if self.steps > self.max_steps: raise Exception("Step limit exceeded (infinite loop or too complex)")

1. F1(n) = n + 1 (a simple increment function)
2. F2(n) = 2n (a linear function)
3. F3(n) = 2^n (an exponential function)
4. F4(n) = 2^(2^n) (a double exponential function)
5. F5(n) = 2^(2^(2^n)) (a triple exponential function)