The laws of Boolean algebra therefore constitute the equational theory of the Boolean prototype.
2.
The equational theory of an algebra is the set of all equations satisfied by the algebra.
3.
An equational theory in a given language consists of equations between terms built up from variables using symbols of that language.
4.
It follows that even among the finite Heyting algebras there exist infinitely many that are subdirectly irreducible, no two of which have the same equational theory.
5.
Each of these three properties can be axiomatized with finitely many equations, whence these equations taken together constitute a finite axiomatization of the equational theory of Boolean algebras.
6.
Wayne Snyder gave a generalization of both higher-order unification and E-unification, i . e . an algorithm to unify lambda-terms modulo an equational theory.
7.
F-coalgebras are dual to variety, so does the class of all F-coalgebras satisfying a given equational theory form a covariety, where the signature is given by F.
8.
In universal algebra and equational theory, the methods of term rewriting, congruence closure and theory is decidable or not depends whether the theory is variable-free or on other conditions.
9.
In his " Feasibly Constructive Proofs and the Propositional Calculus " paper published in 1975, he introduced the equational theory PV ( standing for Polynomial-time Verifiable ) to formalize the notion of proofs using only polynomial-time concepts.
10.
In this way we have translated the commuting diagrams of that category, as the equational theory of Boolean algebras, into the equational consequences of "'A1 "'as the logical representation of that particular composition law.
मोबाइल