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 negation
•
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 $\\mathbf{L}^{\\prime}$ is stronger than $\\mathbf{L}$ or as strong if every class of structures definable in $\\mathbf{L}$ is also definable in $\\mathbf{L}^{\\prime}$ .

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 negation • 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 $\\mathbf{L}^{\\prime}$ is stronger than $\\mathbf{L}$ or as strong if every class of structures definable in $\\mathbf{L}$ is also definable in $\\mathbf{L}^{\\prime}$ .
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