An algebraic construction discovered by logicians Adolf Lindenbaum (1904–1941) and Alfred Tarski (1901–1983) that for many deductive systems $\text{L}$ yields an algebra ${\mathcal{ℒ}}_{\text{L}}\left(T\right)$ for each $\text{L}$-theory $T$. Define an equivalence relation $\sim$ on the language of $T$ defined so that $\phi \sim \psi$ precisely when both $T,\phi {⊢}_{\text{L}}\psi$ and $T,\psi {⊢}_{\text{L}}\phi$ hold, i.e., $\phi$ and $\psi$ are deductively equivalent with respect to $T$. Then the equivalence classes of sentences under $\sim$, i.e., elements $\text{⟦}\phi \text{⟧}=\left\{\xi \mid \phi \sim \xi \right\}$, make up the elements of the algebra ${\mathcal{ℒ}}_{\text{L}}\left(T\right)$, which may be ordered so that for two elements $\text{⟦}\phi \text{⟧}$ and $\text{⟦}\psi \text{⟧}$, $\text{⟦}\phi \text{⟧}\preccurlyeq \text{⟦}\psi \text{⟧}$ whenever $T,\phi {⊢}_{\text{L}}\psi$. When $\text{L}$ permits such constructions (i.e., is algebraizable), operations on ${\mathcal{ℒ}}_{\text{L}}\left(T\right)$ can be defined for each connective. For example, conjunction $\text{⟦}\phi \wedge \psi \text{⟧}$ is the greatest lower bound of $\text{⟦}\phi \text{⟧}$ and $\text{⟦}\psi \text{⟧}$ with respect to $\preccurlyeq$.