Mahler's compactness theorem

Mahler's compactness theorem is a result in the field of mathematical logic, specifically in model theory. The theorem deals with the idea of compactness in relation to sets of first-order sentences. It essentially states that if every finite subset of a set of first-order sentences is satisfiable (i.e., there exists a model that satisfies all the sentences in that finite subset), then the entire set of sentences is also satisfiable.