The Los-Tarski Theorem states that a first-order theory is preserved under taking substructures, meaning every substructure of a model of the theory is again a model of the theory, if and only if the theory can be axiomatized entirely by universal sentences, those built using only universal quantifiers over a quantifier-free formula. Named for Jerzy Los and Alfred Tarski, it is a classical preservation theorem of model theory.
Facts
StatementA first-order sentence is preserved under substructures if and only if it is logically equivalent to a universal sentence. 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 Los Tarski preservation theorem (Wikipedia)
Sources
1. Los Tarski preservation theorem (Wikipedia)
Statement
It states that a first-order sentence is preserved under substructures if and only if it is logically equivalent to a universal sentence.
In Branch: Model Theory, Lead sentence
substructure preservation theorem, is a result in model theory that states the first-order properties are preserved when passing t
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.