Definition:Extension of Class

This page is about Extension of Class. For other uses, see Extension.

Definition

Let $A$ and $B$ be classes.

$B$ is an extension of $A$ if and only if:

$A \subseteq B$

Immediate Extension

$B$ is an immediate extension of $A$ if and only if $B$ contains exactly one more element than $A$.

Also see

• Results about class extensions can be found here.

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 $\text {II}$ -- Maximal principles: $\S 6$ Another approach to maximal principles