---
title: "Birkhoff's theorem (equational logic)"
chunk: 1/1
source: "https://en.wikipedia.org/wiki/Birkhoff's_theorem_(equational_logic)"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:56:18.498364+00:00"
instance: "kb-cron"
---

In logic, Birkhoff's theorem in equational logic states that an equality t = u is a semantic consequence of a set of equalities E, if and only if t = u can be proven from the set of equalities. It is named after Garrett Birkhoff.


== References ==