Lindstrom's Theorem characterizes first-order logic as the strongest logic, among logics extending it, that satisfies both the compactness property and the downward Lowenheim-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 Lowenheim-Skolem property. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Lindstrom's theorem, Wikipedia
Sources
1. Lindstrom's theorem, Wikipedia
Lead section, first sentence
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) Lowenheim-Skolem property.
Lead section, parenthetical
Per Lindstrom, who published it in 1969
- In Branch: Logic and Foundations, Lead sentence
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