User blog comment:Nayuta Ito/Is this bigger than Rayo's number?/@comment-27513631-20180504234554/@comment-25337554-20180505011731

I asked. Here are the answers:

>The definition is very inelegant and somewhat hard to understand. Defining terms of FOL by numbers directly is an ugly method; I recommend context-free grammars.

The competition assumes ZFC, so he used numbers so that the symbols in FOL cannot be confused with the ones in ZFC.

>The system is proof-based and is hence much weaker than Rayo's number. See "is not provable with A" in the definition of f

Just involving proof does not make the number small.

>The system, as translated, isn't really well-defined - there are no definitions of what 16, 48 and 80 are? I assume that 16 is xor, 48 is uniqueness quantifier, and 80 is true, as these are the obvious choices.

The interpretation of 16,48,80 is unique in which FOL' becomes a formal language of first-order predicate logic.