Regular Entailment Relations

Abstract

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 à la Lorenzen and show that the remarkable regularisation process he invented 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”.