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”.
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Acknowledgements
The authors thank the Hausdorff Research Institute for Mathematics for its hospitality and for providing an excellent research environment in May and June 2018; part of this research has been done during its Trimester Program Types, Sets and Constructions.
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Coquand, T., Lombardi, H., Neuwirth, S. (2021). Regular Entailment Relations. In: Heinzmann, G., Wolters, G. (eds) Paul Lorenzen -- Mathematician and Logician. Logic, Epistemology, and the Unity of Science, vol 51. Springer, Cham. https://doi.org/10.1007/978-3-030-65824-3_7
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