Lindström’s theorem
One of the very first results of the study of model theoretic logics is a characterization theorem due to Per Lindström. He showed that the classical first order logic is the strongest logic having the following properties
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Being closed under contradictory negation
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Compactness
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Löwenheim-Skolem theorem
also, he showed that first order logic can be characterised as the strongest logic for which the following hold
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Completeness (r.e. axiomatisability)
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Löwenheim-Skolem theorem
The notion of “strength” used here is as follows. A logic is stronger than or as strong if every class of structures definable in is also definable in .