Little Bigeddon

Little Bigeddon is a googolism based on an extension of the language of set theory. It was defined on the 5th January 2016 by user Emlightened. User LittlePeng9, the creator of BIG FOOT, wrote "... I'd say this is a large number worth losing to ..." on the original blog post. It is likely, therefore, that Little Bigeddon is larger than BIG FOOT, the current largest number.

Definition of Little Bigeddon
It adds an extra sort and trinary truth predicate to the language of set theory, and defines itself as "\(The largest number k such that there is some unary formula φ in the language L={∈,T} of quantifier rank ≤12↑↑12 such that ∃!a(φ(a))∧φ(k)\)."