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 Downward Löwenheim-Skolem property.

Comparing logics

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

References

• The Blackwell Guide to Philosophical Logic, ed. Lou Goble, Blackwell Publishing Inc., 2001.
• Ebbinghaus, H.-D.; J.Flum, W. Thomas (1994). Mathematical Logic. 2nd Edition,