Cowan's theorem is a result in the field of mathematical logic, specifically concerning the structure of certain types of models. It states that if a model of a theory is countable, then any two countable models of that theory are elementarily equivalent, meaning they satisfy the same first-order properties. This theorem helps in understanding the relationships between different models of a given theory. The theorem is named after the mathematician William Cowan, who contributed to model theory. It highlights the significance of countability in logic, showing that countable models can be treated similarly in terms of their logical properties, which is a key concept in the study of model theory.