Theorem

Lindstrom's Theorem

Logic and Foundations

Lindstrom's Theorem characterizes first-order logic as the strongest logic, among logics extending it, that satisfies both the compactness property and the downward Löwenheim-Skolem property. Named for Per Lindstrom, it is a foundational result of abstract model theory explaining why first-order logic occupies a special place among possible logical systems rather than being merely one convenient choice.

Facts

Statement

First order logic is the strongest logic, subject to certain closure conditions such as closure under classical negation, that has both the countable compactness property and the downward Löwenheim-Skolem property. 1

Proof Year

1969 1

Classification

Statement Form

Characterization Theorem 1

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Characterization

In Branch

Logic and Foundations

Source Lindstrom's theorem, Wikipedia

Proved By

Per Lindström

Source Lindstrom's theorem, Wikipedia

Sources

1. Lindstrom's theorem, Wikipedia

Lead section
In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the strongest logic (satisfying certain conditions, e.g. closure under classical negation) having both the (countable) compactness property and the (downward) Löwenheim-Skolem property.
In Branch: Logic and Foundations, Lead sentence
Proved By: Per Lindström, Lead
Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969)

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Lindstrom's Theorem

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