Ok so how would you quantify the statement that there is finite number of twin primes like using there exists, for all, free and bound variables. I know it is an open question but this is just hypothetical
What about the following:
Suppose our variables and constants are taken from the natural numbers and let $\displaystyle P(n)\,,\,n\in\mathbb{N}$ be the statement "n is a prime number":
$\displaystyle \exists M\!\!\in\!\mathbb{N}\;\forall a\!\!\in\!\mathbb{N}\left(P(a)\wedge P(a+2)\rightarrow a<M\right)$
Tonio