[FOM] Another historical query

Charles Parsons parsons2 at fas.harvard.edu
Mon Sep 8 11:14:00 EDT 2008

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

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