Is there an $\mathcal{L}_{\omega_1\omega}$ formula or set of formulas that characterizes the rationals $\mathbb{Q}$ among other number fields?
EDIT: My formula must not contain an infinite number of constants from $\mathbb{Q}$.
Is there an $\mathcal{L}_{\omega_1\omega}$ formula or set of formulas that characterizes the rationals $\mathbb{Q}$ among other number fields? EDIT: My formula must not contain an infinite number of constants from $\mathbb{Q}$. 

