Definition:Type M Set

Definition

Let $S$ be a set of sets.

$S$ is said to be of type $M$ if and only if every element of $S$ is a subset of a maximal element of $S$ under the subset relation.

Also see

• Results about type $M$ sets can be found here.

Linguistic Note

The term Type $M$ appears to have been coined by Raymond M. Smullyan and Melvin Fitting for their Set Theory and the Continuum Problem, revised ed.

Its use on $\mathsf{Pr} \infty \mathsf{fWiki}$ is therefore expected be limited to those pages arising directly from concepts raised as a result of that work.

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: $\S 5$ Maximal principles