 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.