[spam][crazy][fiction][random] Non-Canon MCBoss Spinoffs

mailbombbin mailbombbin at gmail.com
Wed Sep 13 13:53:36 PDT 2023


> To prove the theorem, we proceed by contradiction and assume that an L-formula
> True(n) exists which is true for the natural number n in N if and only if n is the
> Gödel number of a sentence in L that is true in N. We could then use True(n) to
> define a new L-formula S(m) which is true for the natural number m if and only if m
> is the Gödel number of a formula phi(x) (with a free variable x) such that phi(m) is
> false when interpreted in N (i.e. the formula phi(x), when applied to its own Gödel
> number, yields a false statement). If we now consider the Gödel number g of the
> formula S(m), and ask whether the sentence S(g) is true in N, we obtain a
> contradiction. (This is known as a [[Diagonal lemma|diagonal argument]].)


More information about the cypherpunks mailing list