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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LöwenheimSkolem 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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LöwenheimSkolem theorem
The notion of “strength” used here is as follows. A logic ${\mathbf{L}}^{\prime}$ is stronger than $\mathbf{L}$ or as strong if every class of structures^{} definable in $\mathbf{L}$ is also definable in ${\mathbf{L}}^{\prime}$.
Title  Lindström’s theorem 

Canonical name  LindstromsTheorem 
Date of creation  20130322 13:49:30 
Last modified on  20130322 13:49:30 
Owner  mathcam (2727) 
Last modified by  mathcam (2727) 
Numerical id  8 
Author  mathcam (2727) 
Entry type  Theorem 
Classification  msc 03B10 