Kurt Gödel Research Center

2004 seminar talk: Zermelo and Set Theory

Talk held by Akihiro Kanamori (Mathematics Department, Boston University) at the KGRC seminar on 2004-01-09.

Abstract

Ernst Friedrich Ferdinand Zermelo (1871--1953) transformed the set theory of Cantor and Dedekind into {\it abstract} set theory in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization, and thereby tempered the ontological thrust of early set theory and established the basic conceptual framework for the development of modern set theory. Two decades later Zermelo promoted a distinctive cumulative hierarchy view of models of set theory that would have a modern resonance. In this paper Zermelo's published mathematical work in set theory is described and analyzed in its historical context, with the hindsight afforded by the knowledge of what has endured in the subsequent development of set theory. Much can be and has been written about philosophical and biographical issues and about the reception of the Axiom of Choice, and we will refer and defer to others, staying the course through the decidedly mathematical themes and details.