FOST function

FOST(x) is a mathematical function created with the goal of defining the largest numbers possible.
FOST(x) in a sense represents the limits of mathematics. Defining FOST(x) is difficult, and touches upon computation theory, set theory, and formal logic. Roughly speaking FOST(x) is the smallest number not "nameable" in some standard mathematics using x symbols, where "nameable" has an intricate definition, involving formal logic to express the idea of "the largest number that satisfies a special type of assertion, but with a limited number of symbols". The "nameable" requirement prevents Berry's paradox (e.g. the smallest number that can be described only with at least 1000 words).
FOST(x) is specifically defined at [http://www.mrob.com/pub/math/largenum-7.html Large Numbers at MROB (page 7)], where it is compared to the Busy Beaver function.
The MROB page states: "If you're interested in defining larger functions, go right ahead, please check your new function carefully to see if it really pushes the limits a significant amount. If you only use the methods described on these pages, then your new function will not push the limits a significant amount."
To "go outside of mathematics", we can define to exist a larger class of functions, as an axiom (analogous to a Large Cardinal Axiom). This would be very vague, too vague to be absorbed into the definition of FOST(x).

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