Lorenzen Between Gentzen and Schütte

Author:

Kahle Reinhard,Oitavem Isabel

Abstract

AbstractWe discuss Lorenzen’s consistency proof for ramified type theory without reducibility, published in 1951, in its historical context and highlight Lorenzen’s contribution to the development of modern proof theory, notably by the introduction of the $$\omega $$ ω -rule.

Publisher

Springer International Publishing

Reference42 articles.

1. Bernays, P. (1964). On platonism in mathematics. Philosophy of mathematics, edited by Paul Benacerraf and Hilary Putnam, pages 274–286. Prentice-Hall. Lecture delivered June 18, 1934, in the cycle of Conferences internationales des sciences mathematiques organized by the University of Geneva, in the series on Mathematical Logic. Translated from the French by C. D. Parsons from L’enseignement mathematique, 1st ser., vol. 34 (1935), pp. 52–69.

2. Carnap, R. (1935). Ein Gültigkeitskriterium für die Sätze der klassischen Mathematik. Monatshefte für Mathematik und Physik, 42, 163–190.

3. Coquand, T. (2020). Lorenzen and constructive mathematics (pp. 45–59).

4. Coquand, T., Lombardi, H., & Neuwirth, S. (2020). Regular entailment relations (pp. 101–122).

5. Coquand, T., & Stefan N. (2017). An introduction to Lorenzen’s Algebraic and logistic investigations on free lattices (1951). arXiv: 1711.06139v1 [math.LO].

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