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
StatementFirst 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 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Lindstrom's theorem, Wikipedia
Principal Result Of
Source Wikipedia: Per Lindström
Proved By
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)
View the SourceWikipedia: Per Lindström
Principal Result Of: Per Lindström, Article textQuote, Principal Result Of: Per Lindström, Article text
Per "Pelle" Lindström (9 April 1936-21 August 2009, Gothenburg) was a Swedish logician, after whom Lindström's theorem and the Lindström quantifier are named.
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