Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In logic, a pseudoelementary class is a class of structures derived from an elementary class (one definable in first order logic) by omitting some of its sorts and relations. It is the mathematical logic counterpart of the notion in category theory of (the codomain 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. A pseudoelementary class is a reduct of an elementary class. That is, it is obtained by omitting some of the sorts and relations of the given class.

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