Tarski's theorem on the completeness of algebraic theories

Tarski's theorem on the completeness of algebraic theories states that for certain logical systems, if a statement is true in every possible interpretation that satisfies the theory (semantically valid), then it can also be proven using the theory’s rules (syntactically derivable). In essence, it ensures that the formal system is powerful enough to capture all true statements about the structures it describes, meaning no true statement is left unprovable within the theory. This establishes a harmony between what is true in all models and what can be formally proven.