Zermelo s1931e

pp. 502-515

in: Ernst Zermelo, Set theory, miscellanea / Mengenlehre, varia, Berlin, Springer, 2010

Abstract

In this series of short notes found in the Nachlass, Zermelo articulates his late views on and approach to the ordinal numbers. These views encompass the boundary numbers of 1930a and are related to his project of making evident the consistency of set theory "by means of the systematic construction of a "set-theoretic model' using "the unlimited number series' ", as stated at the end of his s1930d. Like his s1930e "On the set-theoretic model", the notes here are carefully typed. On the other hand, they are disparate sketches with redundancies and different emphases. Although Zermelo had sketched the rudiments of the von Neumann ordinals perhaps as early as 1913 and had applied this specific representation of the Cantorian ordinal numbers in his 1930a, he does not appeal to this reduction but pursues the ordinal numbers ab initio as autonomous concept.