👉 MacDougall's theorem, named after Sir Robert Douglas MacDougall, is a fundamental result in mathematical logic and set theory that establishes the consistency of certain axiomatic systems. It states that any consistent system of first-order predicate calculus (including Peano arithmetic) must have at least one model that is not an interpretation of the system itself. This theorem is crucial for understanding how to construct models of certain theories, particularly those involving infinite sets or infinite logical connectives.