Lindström's theorem

In mathematical logic, Lindström's theorem states that first-order logic is the strongest logic (satisfying certain conditions, e.g. closure under classical negation) having both the compactness property and the Löwenheim-Skolem property.

Comparing logics
A logic $$\mathcal{L}'$$ is said to be as strong as $$\mathcal{L}$$ iff every elementary class in $$\mathcal{L}$$ is elementary class in $$\mathcal{L}'$$. In symbols $$\mathcal{L}'\ge\mathcal{L}$$.