# Admissible set

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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.

## References

• Barwise, Jon (1975). Admissible Sets and Structures: An Approach to Definability Theory, Perspectives in Mathematical Logic, Volume 7, Springer-Verlag. Electronic version on Project Euclid.