Clone Theory and Algebraic Logic

Zhaohua Luo

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arXiv · 0907.4531

Clone Theory and Algebraic Logic

Zhaohua Luo

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Abstract

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.

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Zhaohua Luo. 2009-07-27. Clone Theory and Algebraic Logic. https://arxiv.org/abs/0907.4531

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