The class of sets where the embeddings are injective functions and the amalgam is simply the union of the two sets.

Assuming sufficient determinacy, the class of inductive sets has the scale property and thus the prewellordering property.

The class of decidable sets has numerous closure properties.

In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms.

Let be a class (called a simple game and thought of as a property) of recursive sets.

Every class of nonempty sets has a choice function.

It is , the class of hereditarily finite sets, with the inherited element relation.

Likewise, an ordinal number is an equivalence class of well-ordered sets.

In set theory, which is capable of acting as an axiomatic foundation for modern mathematics, natural numbers can be represented by classes of equivalent sets.

In fact, it is analytic, and complete in the class of analytic sets.