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 is larger than BIG FOOT.
Disregarding naive extensions, Little Bigeddon is generally considered the largest named number. However, Oblivion, Utter Oblivion, and any Oblivion-based functions could be considered larger than Little Bigeddon, but it is questionable if they are sufficiently well-defined, and sufficiently compliant to the basic rules of googology, to take that title.
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 \(\exists\lnot a(\varphi(a))\land\varphi(k)\).
Sources
- ↑ Emlightened. Little Bigeddon. Large Ordinums.
- ↑ Emlightened. Little Bigeddon.