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arXiv · 1301.0667

Algebraic Logic, I Quantifier Theories and Completeness Theorems

Zhaohua Luo
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Abstract

Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the category of a monad of sets to the category of Boolean algebras, together with a uniquely determined system of quantifiers. A striking feature of this approach is that Cayley's Completeness Theorem and Godel's Completeness Theorem can be stated and proved in a much simpler fashion for quantifier theories. Both theorems are due to Halmos for polyadic algebras. We also present a simple transparent treatment of ultraproducts of models of a quantifier theory.

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Zhaohua Luo. 2013-01-04. Algebraic Logic, I Quantifier Theories and Completeness Theorems. https://arxiv.org/abs/1301.0667

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