[FOM] Problem on order types

Jeremy Clark jeremy.clark at wanadoo.fr
Sat Mar 5 15:48:21 EST 2005

Since we're in FOM, I think it is only fair to be pedantic and say that 
the answer is only a finite integer if you assume the law of excluded 
middle. To an intuitionist there are many such sets, but I do not know 
if a cardinal can be assigned to the class of all such. (Can anyone 
enlighten me on this question?) Certainly not a finite one in any case. 
If you do assume excluded middle (many don't) then the answer is 11. I 
think. (If I am wrong then my excuse is that I don't like to assume 
excluded middle. If I am right then please ignore the contents of these 


Jeremy Clark

On Mar 5, 2005, at 5:27 am, JoeShipman at aol.com wrote:

> Here's a cute problem.  The answer is a finite integer, but it's very 
> easy to get it wrong.
> Let X be an ordered set such that
> for all a<b in X, (a,b) is order-isomorphic to the rational numbers.
> How many possibilities are there for the order type of X?
> -- JS
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