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 𝐋 is stronger than 𝐋 or as strong if every class of structuresMathworldPlanetmath definable in 𝐋 is also definable in 𝐋.

Title Lindström’s theorem
Canonical name LindstromsTheorem
Date of creation 2013-03-22 13:49:30
Last modified on 2013-03-22 13:49:30
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 8
Author mathcam (2727)
Entry type Theorem
Classification msc 03B10