# Stefan Neuwirth

- March 2017

###### Paul Lorenzen: logic and algebra

Lorenzen discovered before 1944 that endowing a preordered set with a system of ideals has the same formal structure as proving the non-contradiction of a logical calculus. This discovery had as effect a new definition of a system of ideals as a logical calculus: a so-called single-conclusion entailment relation, ideated by Paul Hertz in 1923.

We shall tell this episode of the years 1939-1951 and show how this approach enables the development of divisibility theory of an integral domain without set theory.