Definition:Intersection of Special Subsets

Definition

Let $g$ be a progressing mapping.

Let $x$ be a set.

Let $\powerset x$ denote the power set of $x$.

Let $A$ be the class of all $x$-special subsets of $\powerset x$ with respect to $g$.

We denote by $M_x$ the intersection of $A$:

$M_x = \ds \bigcap A$

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 $\text {III}$ -- The existence of minimally superinductive classes: $\S 7$ Cowen's theorem: Definition $7.3$