[FOM] Another historical query

[Charles Parsons]

On Sep 6, 2008, at 7:54 PM, Thomas Forster wrote:

>
> The von Neumann ordinals are precisely the (wellfounded) hereditarily
> transitive sets.   Does anyone on this list know who first proved  
> it?  Or
> who first published it?
>
>
>     tf
>
>
>


That characterization occurs in a letter of Bernays to Goedel of 3  
May 1931, in which he outlines his system of axiomatic set theory.  
See Goedel, Collected Works, vol. IV, p. 112. So I assume it was  
Bernays who first proved it. (His axiomatization included Foundation.)

But I don't know when or how it first got into print.

Interestingly, the term Bernays uses that is translated as  
'transitive' is 'vollzaehlig'. I seem to recall that in earlier years  
the term 'complete' was used. That probably echoes Bernays' term,  
which was very likely used by other writers in German.

Charles Parsons