[FOM] Some historical questions

G. Aldo Antonelli antonelli at ucdavis.edu
Sun Nov 7 13:15:46 EST 2010

On 11/7/10 9:00 AM, fom-request at cs.nyu.edu wrote:

> 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.

It's known that, in general, unordered pairs (= symmetric irreflexive 
binary relations) can be used to encode arbitrary binary relations. The 
reference I have is the following:

Anil Nerode and Richard Shore [1980], Second order logic and theories of 
reducibility orderings, The Kleene symposium (Jon Barwise, H. Jerome 
Keisler, and Kenneth Kunen, editors), North-Holland, Amsterdam, pp. 181-200.

-- Aldo

G. Aldo Antonelli
Professor of Philosophy
University of California, Davis
antonelli at ucdavis.edu, +1 530 554 1368

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