---
tag: BJWNDECQQ4
kind: concept
name: Hereditarily
sources:
  - wikipedia: en:43580500@r1360947732
    locator: Glossary of set theory, section H
    note: adopted
    mention: wikipedia://en/43580500#HA1U
    sections: [Summary]
inventory: [CK3BAT2NT8]
---

## Summary

If *P* is a property the a set is hereditarily *P* if all elements of its transitive closure have property *P*. Examples: Hereditarily countable set Hereditarily finite set