L-sentence for finite degree of algebraic extension of $\mathbb{Q}$

Question

Let $L=\{0,1,+,-, \cdot \}$ be the language.

This is follow up question on: Axiomatize purely transcendental field extension.

I'm trying to write an L-sentence that says" the algebraic extension of $\mathbb{Q}$ is at least of degree $n$.

But I'm not sure how to proceed.

Some thoughts:

• We need to have some distinct $\phi_i$ finite extensions.
• We need to include some properties of finite extension... but I'm not sure what they are.

Thanks in advance!