User blog:Ubersketch/Uncomputable function

We define a language (Weak set language) using only a few symbols:

x - Variable. It can be a statement or set.

Tx - Statement x is true. (x is a statement)

Nx - If x is true, then Nx is not true and vice versa. (x is a statement)

Sxyz - z is true if x or y is false. (x, y, and z are statements)

Exy - x is an element of y. (x and y are sets)

Uxy - For all x, x satisfies y. (x and y are sets)

Then we declare initial axioms (Weak set theory):

NEx0

UxE0x

Then we create an automaton (Strong automaton):

A strong automaton is a 5-tuple 

Q - A set of states.

S - A set of symbols.

D - The transition function. D:Q and S -> Q

B - State of the automaton before anything has been processed.

F - Set of states where the automaton accepts. (Infinite time may pass before the automaton accepts a certain input.)

WST(n) is the largest finite number (set with transitive relation) provably definable in WSL assuming the axioms of WST and any axioms declared by any Tx in the string of symbols where provably definable means it can be proven by a strong automaton using at most n symbols, outputting 0 if it cannot create a number using any amount of statements with >=n symbols.