# 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

also, he showed that first order logic can be characterised as the strongest logic for which the following hold

• Completeness (r.e. axiomatisability)

• Löwenheim-Skolem 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 LindstromsTheorem 2013-03-22 13:49:30 2013-03-22 13:49:30 mathcam (2727) mathcam (2727) 8 mathcam (2727) Theorem msc 03B10