The following lemma shows that transitive sets play a prominent role in the set theory. They are omnipresent.

**Lemma**: Any Set is Subset of Some Transitive Set - Its Transitive Hull

For every set $X$ there exists a transitive set $Y$, such that $X$ is a subset of $Y,$ formally $X\subseteq Y.$ This set is called the **transitive hull** of the set $X$.

| | | | | created: 2019-01-29 22:37:06 | modified: 2019-01-29 23:50:56 | by: *bookofproofs* | references: [8055]

## 1.**Proof**: *(related to "Any Set is Subset of Some Transitive Set - Its Transitive Hull")*

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[8055] **Hoffmann, D.**: “Forcing, Eine EinfÃ¼hrung in die Mathematik der UnabhÃ¤ngigkeitsbeweise”, Hoffmann, D., 2018

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