Lindström's theorem

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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.

[edit] 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 $\mathcal{L}'\ge\mathcal{L}$ .

[edit] 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. ISBN 0-387-94258-0.

$\lnot(p\land\lnot p)$