Universal Algebra and Mathematical Logic
Logic
2011-04-26 v1 Formal Languages and Automata Theory
Logic in Computer Science
Abstract
In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of parameters in a standard way. The free right algebra F(L, C) of formulas over T(L, C) is then generated by atomic formulas. Structures for L over C are represented as perfect valuations of F(L, C), and theories of L are represented as filters of F(L). Finally Godel's completeness theorem and first incompleteness theorem are stated as expected.
Cite
@article{arxiv.1104.4606,
title = {Universal Algebra and Mathematical Logic},
author = {Zhaohua Luo},
journal= {arXiv preprint arXiv:1104.4606},
year = {2011}
}