Definition:Proper Lower Section (Class Theory)

Definition

Let $A$ be a class under a total ordering $\preccurlyeq$.

Let $L$ be a lower section of $A$ such that:

$L \ne \O$

$L \ne A$

Then $L$ is known as a proper lower section of $A$ (by $L$).

Also see

• Definition:Lower Section (Class Theory)

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 1$ Introduction to well ordering: Exercise $1.2$
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $6$: Order Isomorphism and Transfinite Recursion: $\S 1$ A few preliminaries