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Pseudoelementary class

In logic, a pseudoelementary class is a class of structures derived from an elementary class by omitting some of its sorts and relations. It is the mathematical logic counterpart of the notion in category theory of a forgetful functor, and in physics of (hypothesized) hidden variable theories purporting to explain quantum mechanics. Elementary classes are (vacuously) pseudoelementary but the converse is not always true; nevertheless pseudoelementary classes share some of the properties of elementary classes such as being closed under ultraproducts.