Universal Algebra and Mathematical Logic

Zhaohua Luo

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arXiv · 1104.4606

Universal Algebra and Mathematical Logic

Zhaohua Luo

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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.

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BibTeX RIS

Zhaohua Luo. 2011-04-24. Universal Algebra and Mathematical Logic. https://arxiv.org/abs/1104.4606

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