nLab extension (semantics)

This entry is about the notion of extension in semantics. For the notion of extension in algebra, see there.

Idea

Given a proposition $P$ on terms of type $X$, its extension is the type $\{x \in X | P(x)\}$ of all elements $x$ for which $P(x)$ is true.

Related entries

• extensional type theory

• comprehension

References

• wikipedia, extension (semantics)