compactness theorem

The Compactness Theorem in logic states that if every small subset of a collection of statements (finite parts) can be true at the same time, then the entire collection of statements can also be true together. In simple terms, it means that if there's no contradiction in any small group of these statements, then there's a way for all of them to be true simultaneously. This helps in understanding larger systems by examining their smaller parts, ensuring consistency and revealing the possibility of a comprehensive solution or model.