Godel's completeness theorem

Gödel's Completeness Theorem states that if a logical statement is universally true in all possible scenarios, then there is a formal proof of that statement within a given logical system. In other words, if something is logically valid, it can be mathematically proven within the system. This establishes a connection between truth in all models (semantics) and provability within a system (syntax), confirming that logical systems are capable of capturing all universally valid truths through formal proof processes.