Largest valid googologism

The title of largest valid googologism has belonged to various numbers.

For a long period, Rayo's number, which is defined as the smallest number larger than any number expressible in the language of first-order set theory in a googol \(10^{100}\) symbols or less, was uncontestedly considered the largest valid googologism; however, it was later upstaged by Fish number 7, which has been criticized as being overly clunky and not increasing the value enough to not classify as not being a naive extension, and was not really recognized as the largest valid googologism. Fish number 7 adds an oracle formula to the original microlanguage used to define Rayo's number.

BIG FOOT was created later by Wojowu, and completely dethroned Rayo's number. This number diagonalizes over a generalization of nth-order set theory known as first-order oodle theory, and is enormously larger than Rayo's number. It was fully recognized by the googology community as the new record-holder for largest valid googologism.

Jonathan Bowers created two numbers, Oblivion and Utter Oblivion, which diagonalize over the fundamental concept of a mathematical system as a whole, and claimed that they were larger than both BIG FOOT and Rayo's number, as well as Fish number 7. However, he only gave a broad outline of his definitions, rather than describing the numbers using proper mathematical rigor.

Little Bigeddon is considered the current holder of the title of largest valid googologism. It was coined by Googology Wiki user User:Emlightened, and diagonalizes over an extension of set theory which contains an additional kind of variable known as a rank variable.