FOM: Zermelo's successor function

[Robert Black]

It's at the end of the first section of the famous 1908 paper 
'Untersuchungen ueber die Grundlagen der Mengenlehre I' (translation 
in the van Heijenoort collection). Zermelo gives the axiom of 
infinity in the form that there's a set containing the empty set and 
closed under the formation of singletons, and then identifies the 
minimal such set with the number sequence.

Robert

>Dear FOM'ers,
>
>I underdstand that E. Zermelo first suggested representing Peano's successor
>function by the set theoretic operation of forming singletons (?). Can
>anyone on the list verify this; if so, is a citation available?
>
>Many Thanks,
>
>Peter A.
>Toronto


-- 
Robert Black
Dept of Philosophy
University of Nottingham
Nottingham NG7 2RD

tel. 0115-951 5845