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
In Branch
Source Los Tarski preservation theorem (Wikipedia)
Proved By
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
Proved By: Alfred Tarski, Lead section
The theorem is named after Jerzy Łoś and Alfred Tarski.
In Group: Mathematical Logic and Model Theory, Lead section
or substructure preservation theorem, is a result in model theory that states the first-order properties are preserved
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.