Definition:Special Set
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Definition
Let $g$ be a progressing mapping.
Let $S$ and $x$ be sets.
We say that:
- $S$ is special for $x$ (with respect to $g$)
\((1)\) | $:$ | $\O \in S$ | |||||||
\((2)\) | $:$ | $S$ is closed under $g$ relative to $x$ | |||||||
\((3)\) | $:$ | $S$ is closed under chain unions |
Also known as
Instead of $S$ is special for $x$, we can say $S$ is $x$-special.
Also see
- Results about special sets 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 $\text {III}$ -- The existence of minimally superinductive classes: $\S 7$ Cowen's theorem: Definition $7.2$