User blog:--MULLIGANACEOUS--/The YETI function, regarding Oblivion.

After reading Jonathan Bower's post about Oblivion, I came up with a functional analogue of the Rayo's number and the BIG FOOT. Rayo's number can be realized by Rayo's function $$\text{Rayo}(n)$$, where Rayo's number is $$\text{Rayo}(10^{100})$$. Similarly, BIG FOOT can be realized by the FOOT function $$\text{FOOT}(n)$$ where BIG FOOT is $$\text{FOOT}^{10}(10^{100})$$, and the exponent represents functional iteration. We could therefore define an analogous function $$f(n)$$ where Oblivion is $$f(\text{kungulus})$$.

Jonathan Bowers attempted to surpass Rayo, FOOT, and all other functions which diagonalize over the number of symbols used in a n-symbol language by introducing Oblivion. Rayo and FOOT will be evaluated by the number of symbols required to completely describe them; let this be n. He estimated that the value of n for set theory n1 and oodle theory n2 would be at the order of 10000, and n1 < n2. A system completely well-described using n symbols would be a K(n) system - set-theory and oodle-theory would be approximately K(10000) systems, though n is not precisely known.

I implemented the Yeti function $$\text{YETI}_n(m)$$ based on Jonathan Bower's definition of Oblivion and how it connects to Rayo and FOOT. This function represents the largest finite number that can be uniquely definable using m symbols in a K(n) system, or similarly (using Rayo's definition), the smallest finite number larger than any positive integer that can be uniquely definable using m symbols in a K(n) system. $$\text{Rayo}(m) $$ and $$\text{FOOT}(m)$$ can therefore be approximated by $$\text{YETI}_{10000}(m)$$. Oblivion would be defined as $$\text{YETI}_\text{gongulus}(\text{kungulus})$$, and its corresponding function $$f(m)$$ is $$\text{YETI}_\text{gongulus}(m)$$. It is however unknown if Oblivion or the Yeti function is well-defined.