Regular entailment relations

TL;DR

This paper introduces regular entailment relations inspired by Lorenzen's work, establishing a key theorem and connecting them with Lorenzen's systems of ideals through a regularisation process, emphasizing constructive and transparent concepts.

Contribution

It defines regular entailment relations, proves a fundamental theorem, and links them with Lorenzen's ideals via regularisation, advancing the theoretical framework.

Findings

Established a crucial theorem for regular entailment relations

Connected regularisation process with Lorenzen's systems of ideals

Provided constructive objects and arguments for clarity

Abstract

Inspired by the work of Lorenzen on the theory of preordered groups in the forties and fifties, we define regular entailment relations and show a crucial theorem for this structure. We also describe equivariant systems of ideals {\`a} la Lorenzen and show that the remarkable regularisation process invented by him yields a regular entailment relation. By providing constructive objects and arguments, we pursue Lorenzen's aim of "bringing to light the basic, pure concepts in their simple and transparent clarity"