[FOM] counted sets

Thomas Forster T.Forster at dpmms.cam.ac.uk
Tue Aug 18 19:24:11 EDT 2009

On Mon, 17 Aug 2009, Vaughan Pratt wrote:

> Aha, the "counted" terminology is just what I wanted, thanks Thomas. 
> Too bad it's not in wider use.  What's a citation for the term that no 
> Wikipedia editor would complain about, in case it seems worth mentioning 
> in the article on countable sets?
  That's a good question.  I learnt the terminology from Conway in 
Cambridge when i was a Ph.D. student there in a previous millenium
(I've always assumed the expression is his: Conway does have this 
*wonderful* gift for snappy names).   As to where the nomenclature 
first appears in print, God knows.  It's certainly in my u/g text 
*Logic, Induction and Sets*, but that surely cannot be its first 
appearance.   There must surely be *somebody* on this list who is 
based in Princeton and could ask him over coffee one morning?

   Incidentally i think Tim Chow's point about how countable set must 
be a more fundamental notion than counted set (and how a vector space 
is a thing that *has* a basis rather than *comes-equipped-with-a-basis*)
is a good and important one.   To achieve generality, throw away as much
gadgetry from the signature as you can.  After all, that is how we reached 
set theory in the first place - by throwing away everything except bare

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