[FOM] Another historical query
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?
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.
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