Is the non-principal ultraproduct of finite fields $\prod_p \mathbb{F}_p/\sim$ a nonstandard model of the rationals $\mathbb{Q}$?
EDIT: Can we realize $\mathbb{Q}^*$ as an ultraproduct?
# Ultraproduct $\prod_p \mathbb{F}_p/\sim$ and $\mathbb{Q}^*$
Is the non-principal ultraproduct of finite fields $\prod_p \mathbb{F}_p/\sim$ a nonstandard model of the rationals $\mathbb{Q}$?