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Little Bigeddon is a googologism based on an extension of the language of set theory. It was defined on the 5th January 2017 by user Emlightened.[1] User LittlePeng9, the creator of BIG FOOT, wrote "... I'd say this is a large number worth losing to ..." on the original blog post.[2] Little Bigeddon was supposed to be larger than BIG FOOT. Unfortunately, BIG FOOT is ill-defined, and hence this comparison does not make sense.

Disregarding naive extensions, Little Bigeddon was generally considered the largest named number. However, Oblivion, Utter Oblivion, and any Oblivion-based functions could have been considered larger than Little Bigeddon, but it was questionable if they are sufficiently well-defined and sufficiently compliant to the basic rules of googology, to take that title. At last, it has turned out that the definition of Little Bigeddon also includes many errors.

## Definition of Little Bigeddon

To the language of set theory, we add an extra sort of variables, which is called the rank variables, which can be quantified by a designated rank quantifier $$\forall_R$$, and a trinary predicate $$T$$, which is the transfinitely iterated truth predicate. We then define the Little Bigeddon as the largest number $$k$$ such that there is some unary formula $$\varphi$$ in the language $$\mathcal L=\{\in,T\}$$ of quantifier rank $$\leq 12\uparrow\uparrow 12$$ such that $$\exists\lnot a(\varphi(a))\land\varphi(k)$$.

## Issue

The definition contains many errors pointed out by p進大好きbot. For example, there is no $$d \in c$$ satisfying the condition $$\forall e \exists ! f(d = \langle e, f \rangle)$$ in the second line of the definition of $$T$$, i.e. $$T$$ is always false. The Goedel codes $$\ulcorner d = e \urcorner$$ and $$\ulcorner d \in e \urcorner$$ in the fourth and fifth lines do not make sense, and hence seem to be typos of $$\ulcorner x_d = x_e \urcorner$$ and $$\ulcorner x_d \in x_e \urcorner$$. The evaluation $$c(d)$$ in the fouth, fifth, and sixth lines is undefined.

Therefore, strictly speaking, Little Bigeddon is ill-defined unless such massive errors are removed.

## Sources

1. Emlightened. Little BigeddonLarge Ordinums
2. Emlightened. Little Bigeddon