Gödel's completeness theorem

Gödel's completeness theorem states that in classical logic, if a statement is logically true—meaning it must be true in all situations—then there is a formal proof of that statement using the rules of logic. Conversely, if the statement can be proven within the logical system, it is guaranteed to be true in all models or interpretations. In essence, this theorem links the idea of truth in every possible scenario with the ability to formally prove the statement within a given logical framework, ensuring that our proofs align with universal truths.