---
tag: 3BHPBW4WJV
kind: concept
name: Generic
sources:
  - wikipedia: en:43580500@r1360947732
    locator: Glossary of set theory, section G
    note: adopted
    mention: wikipedia://en/43580500#35GP
    sections: [Summary]
inventory: [75QVG9RTXK]
---

## Summary

A generic filter of a poset *P* is a filter that intersects all dense subsets of *P* that are contained in some model *M*.

A generic extension of a model *M* is a model *M*\[*G*\] for some generic filter *G*.