Omega-categorical theory

An omega-categorical theory is a concept from model theory, a branch of mathematical logic. A first-order theory is said to be \(\omega\)-categorical if it has exactly one countable model up to isomorphism. This means that if a theory is \(\omega\)-categorical, any two countable models of this theory will be structurally the same; they can be transformed into each other via a bijective mapping that preserves the relations and functions defined by the theory.