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单词 LindstromsTheorem
释义

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

  • Being closed under contradictory negationMathworldPlanetmath

  • Compactness

  • Löwenheim-Skolem theorem

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.

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更新时间:2025/5/4 16:07:54