# Lindenbaum–Tarski Algebra

### (Algebraic Logic)

Tech

###### Algebraic Logic ## What is Lindenbaum–Tarski algebra?

In mathematical logic, the Lindenbaum–Tarski algebra (or Lindenbaum algebra) of a logical theory T consists of the equivalence classes of sentences of the theory (i.e., the quotient, under the equivalence relation ~ defined such that p ~ q exactly when p and q are provably equivalent in T). That is, two sentences are equivalent if the theory T proves that each implies the other. The Lindenbaum–Tarski algebra is thus the quotient algebra obtained by factoring the algebra of formulas by this congruence relation. The algebra is named for logicians Adolf Lindenbaum and Alfred Tarski. It was first introduced by Tarski in 1935as a device to establish correspondence between classical propositional calculus and Boolean algebras. The Lindenbaum–Tarski algebra is considered the origin of the modern algebraic logic.

### Technology Types

algebraic logicalgebraic structure

### Synonyms

Lindenbaum algebraLindenbaum-Tarski algebra

### Translations

Algèbre de Lindenbaum (fr)Lindenbaumova algebra (cs)Алгебра Линденбаума — Тарского (ru)林登鲍姆-塔斯基代数 (zh)

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— Date merged: 11/6/2021, 1:32:44 PM
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