Admissible set

In set theory, a discipline within mathematics, an admissible set is a transitive set A {displaystyle A,} such that ⟨ A , ∈ ⟩ {displaystyle langle A,in angle } is a model of Kripke–Platek set theory (Barwise 1975). In set theory, a discipline within mathematics, an admissible set is a transitive set A {displaystyle A,} such that ⟨ A , ∈ ⟩ {displaystyle langle A,in angle } 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.