Some Unpublished Letters by G\"odel and von Neumann in the Fraenkel Archive

TL;DR

This paper publishes and discusses previously unpublished letters by G"odel and von Neumann from the Fraenkel Archive, revealing insights into foundational mathematical theories and their historical context.

Contribution

It uncovers and analyzes uncatalogued correspondence that sheds light on G"odel's and von Neumann's foundational work and their intellectual relationships.

Findings

G"odel's letters relate his incompleteness theorem to other foundational work.

Von Neumann's 1923 letter explains his approach to set theory axiomatization.

New archival material provides historical insights into early 20th-century logic.

Abstract

Several letters by Kurt G\"odel and Johann (J\'anos) von Neumann from the (so far uncatalogued) archive of Abraham (Adolf) Fraenkel at the National Library of Israel are published and discussed. These include two fragments by G\"odel of special interest, since they concern the relationship between G\"odel's incompleteness theorem and work by Herbrand, Presburger, and Zermelo, as well as a long letter from von Neumann from 1923 explaining his own approach to the axiomatization of set theory.