Definition:Supercomplete Class

From ProofWiki
Jump to navigation Jump to search


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.