User talk:Vel!/FOST

I have an idea for how to do recursion and ordinal addition. It's kind of convoluted, but I think it will work. More evidence that Rayo's function takes quite a while to really pick up.


 * Define an ordered pair (a, b) = {{a}, {a, b}} (Kuratowski definition) and define formulas car(x) and cdr(x) that extract the first and second elements in ordered pairs.
 * Define a function as a set of ordered pairs; the first element is the input and the second is the output. Define a formula apply(f, x) that calls function f with x as the input.
 * Define the set Add:

∀a: ((a, 0), a) ∈ Add ∀a, b, c: ((a, b), c) ∈ Add ⇔ ((a, Sb), Sc) ∈ Add


 * Define T:

T = apply(Add, (a, b))

FB100Z &bull; talk &bull; contribs 16:41, July 6, 2013 (UTC)