%0 Journal Article
%T Clone Theory and Algebraic Logic
%A Zhaohua Luo
%J Computer Science
%D 2009
%I arXiv
%X The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other. Left and right algebras over a clone are covariant and contravariant functors from the category to that of sets respectively. In this paper we show that first-order logic can be studied effectively using the notions of right and left algebras over a clone. It is easy to translate the classical treatment of logic into our setting and prove all the fundamental theorems of first-order theory algebraically.
%U http://arxiv.org/abs/0907.4531v1