Definition:Supercomplete Class
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Definition
Let $A$ denote a class.
Then $A$ is a supercomplete class if and only if:
\((1)\) | $:$ | $A$ is transitive: | \(\ds \forall x: \forall y:\) | \(\ds \paren {x \in y \land y \in A \implies x \in A} \) | |||||
\((2)\) | $:$ | $A$ is swelled: | \(\ds \forall x: \forall y:\) | \(\ds \paren {x \subseteq y \land y \in A \implies x \in A} \) |
Also see
- Results about supercomplete classes can be found here.
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 2$ Transitivity and supercompleteness