Database: Sethood predicate

Definition 34: By the sethood predicate will mean the unary predicate \underset{y}{\textup{Set}}(x) \hspace{3mm} \textup{defined by} \hspace{3mm} \exists y (x \in y), where the right-side existentially quantified membership statement means x is a set. Should no confusion arise we may omit y , simply writing \textup{Set}(x) and taking for granted that y is distinct from all other variables involved.

This database entry builds on the following:

  1. Terminology: Class, statement
  2. Definition: Existential quantification
  3. Definition: Unary predicate