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Regular entailment relations

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 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"