Infinite field of positive characteristic from an ultraproduct
= Infinite field of positive characteristic from an ultraproduct
For a <prime number> $p$, a <nonprincipal ultrafilter> on $\mathbb N$ gives
$$
K=\prod_{n\geq1}\mathbb F_{p^n}/\mathcal U.
$$
The <Łoś theorem> makes $K$ a <field> of <characteristic of a field>[characteristic] $p$. For every natural number $m$, almost all factors have at least $m$ elements, so $K$ is infinite.