Double extension set theory

Double extension set theory is not a widely recognized term in standard mathematical literature. However, it may refer to a specific concept or methodology in mathematical logic, model theory, or set theory that involves an extension of traditional set theoretic concepts. In general, when we talk about "extension" in set theory, it may refer to either the process of adding new elements to a set or expanding the framework of set theory itself, such as through the development of new axioms or structures.