lindenbaum-tarski algebra

In mathematical logic, the Lindenbaum-Tarski algebra A of a logical theory T consists of the equivalence classes of sentences p of the theory, under the equivalence relation ~ defined by

p ~ q when p and q are logically equivalent in T.

That is, in T q can be deduced from p, and p from q. Operations in A are inherited from those available in T, typically conjunction and disjunction, where they are well-defined on the classes. When negation is present in T, then A is a Boolean algebra, under some mild conditions. Sometimes called simply Lindenbaum algebra, this construction is named for Adolf Lindenbaum (1904-1941 or 1942) and Alfred Tarski.

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