Definition:Nest/Class Theory

Definition

Let $C$ be a class.

$C$ is a nest if and only if:

$\forall x, y \in C: x \subseteq y$ or $y \subseteq x$

Also see

• Definition:Chain (Order Theory)

• Nest under Subset Ordering is Chain

• Results about nests can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 4$ A double induction principle and its applications: Definition $4.5$