Fix a prime number $p$. Is there a first order sentence $\phi_p$ in the language of fields such that $\phi_p$ holds in a number field $K$ if and only if the prime $p$ is unramified in the field extension $K/\mathbb{Q}$?

I THINK, the answer is YES by a paper of Robert Rumely: Undecidability and definability of the theory of global fields, 1980, where he showed that "a great variety of numbertheoretic objects, from rings of integers and valuations, to zetafunctions and adele rings" are definable. Many of them are actually uniformally definable. For the ramification issue, see the bottom of Page 210. 

