[FOM] Some historical questions

Thomas Forster T.Forster at dpmms.cam.ac.uk
Sat Nov 6 05:02:49 EDT 2010

Allen Hazen and i have been in correspondence of late and some historical 
questions have come up, which members of the list might be able to help us 

It's known that Hartogs' theorem can be proved without any use of 
replacement.  Did Hartogs' do it without any replacement?  We know 
replacement wasn't spelled out as an axiom in 1915 but he might have
use it cryptically anyway.  Does anyone on this list know? Does anyone 
have electronic copy of the original? Or of a translation into english 
(or even french!)?

Paul Henrard has a clever way of defining equinumerosity between sets that 
doesn't use ordered pairs, by using overlapping unordered pairs.  Some 
time in the 1970s. I don't *think* he ever published it.  Allen Hazen
independently discovered (essentially) the same trick. Others may have 
done the same.  Does anyone know anywhere where such a gadget is 
published?  It would be good to get the history right.


URL:  www.dpmms.cam.ac.uk/~tf; DPMMS ph: +44-1223-337981;
(UEA ph:  +44-1603-593588; mobile in UK +44-7887-701-562;)

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