Forum:Question about Rayo's number

I have some questions about Rayo's number and FOST.
 * 1) How do we define numbers in FOST? Do we use 0={} and a+1=a∪{a}?
 * 2) How do we know what number a FOST expression defines?
 * 3) What happens if you define function f(x) in FOST such that f(x) is the smallest natural number greater than all natural numbers that can be uniquely identified by a FOST expression of at most x symbols (which is the same as the definition of Rayo's function)? Does that make Rayo's function above a certain value and Rayo's Number ill-defined because of Berry's paradox?