Admissible set

In set theory, a discipline within mathematics, an admissible set is a transitive set $$ A\, $$ such that $$\langle A,\in \rangle$$ is a model of Kripke–Platek set theory (Barwise 1975).

The smallest example of an admissible set is the set of hereditarily finite sets. Another example is the set of hereditarily countable sets.