Ax-Kochen Isomorphism Theorem

Let $P$ be the Set of Primes, and let $\Bbb{Q}_p$ and $Z_p(t)$ be the Fields of p-adic Number and formal Power series over $Z_p=(0, 1, \ldots, p-1)$. Further, suppose that $D$ is a ``nonprincipal maximal filter'' on $P$. Then $\prod_{p\in P}\Bbb{Q}_p/D$ and $\prod_{p\in P} Z_p(t)/D$ are Isomorphic.

See also Hyperreal Number, Nonstandard Analysis