Lindström's theorem

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 Downward 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}'gemathcal{L}.

References

* "The Blackwell Guide to Philosophical Logic", ed. Lou Goble, Blackwell Publishing Inc., 2001.
*


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