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Lindström's theorem
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(Theorem)
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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 $\mathbf{L}'$ is stronger than $\mathbf{L}$ or as strong if every class of structures definable in $\mathbf{L}$ is also definable in $\mathbf{L}'$ .
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Cross-references: definable, structures, class, strong, stronger, compactness, negation, closed under, properties, classical first order logic, theorem, characterization, logics
There is 1 reference to this entry.
This is version 5 of Lindström's theorem, born on 2003-08-06, modified 2005-04-14.
Object id is 4556, canonical name is LindstromsTheorem.
Accessed 2190 times total.
Classification:
| AMS MSC: | 03B10 (Mathematical logic and foundations :: General logic :: Classical first-order logic) |
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Pending Errata and Addenda
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