---
tag: X3G0RG2GPZ
kind: concept
name: Relative consistency proof
sources:
  - wikipedia: en:76765067@r1368301704
    locator: Glossary of logic, section R
    note: adopted
    mention: wikipedia://en/76765067#USYQ
    sections: [Summary]
inventory: [S360P2MY5Y]
---

## Summary

A proof showing that if a mathematical system $S$ is consistent, then an extension of $S$ by adding new axioms is also consistent, used to compare the foundational strength of different theories.