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Book Sections Year : 2021

Regular entailment relations

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 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''
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hal-02418320 , version 1 (18-12-2019)
hal-02418320 , version 2 (08-07-2020)

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Thierry Coquand, Henri Lombardi, Stefan Neuwirth. Regular entailment relations. Gerhard Heinzmann; Gereon Wolters. Paul Lorenzen -- Mathematician and Logician, 51, Springer, pp.103-114, 2021, Logic, Epistemology, and the Unity of Science, 978-3-030-65823-6. ⟨10.1007/978-3-030-65824-3_7⟩. ⟨hal-02418320v2⟩
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