Equivalent Universal Horn Theories. General Algebraic Logic


Academic Paper, 2018

85 Pages, Grade: 3


Abstract or Introduction

The aim of this monograph is to introduce and study a general concept of equivalence between universal Horn theories that would cover on an equal formal basis both Mal'cev's concept of rational equivalence between implicational classes of abstract algebras and our more recent concept of definitional equivalence between finitary universal Horn theories without equality proposed and explored in one of our previous works.

Starting from a formal definition quite naturally generalizing our conception of definitional equivalence, we then advance our generalized notion towards a Mal'cev-style categorical characterization of equivalence justifying our generalization. We also apply our general study to the issues of equivalential and algebraizable universal Horn theories. We also supply our general results with appropriate counterexamples showing that the former cannot be strengthened. At last, we provide an example of a finite finitary infinitely algebraizable universal Horn theory that justifies involving infinitary logic within the context of General Algebraic Logic.

Details

Title
Equivalent Universal Horn Theories. General Algebraic Logic
Grade
3
Author
Year
2018
Pages
85
Catalog Number
V452732
ISBN (eBook)
9783668869455
ISBN (Book)
9783668869462
Language
English
Keywords
model, algebra
Quote paper
Alexej Pynko (Author), 2018, Equivalent Universal Horn Theories. General Algebraic Logic, Munich, GRIN Verlag, https://www.grin.com/document/452732

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