Time for a topological challenge. I saw a suitcase handle with both its loops around a door handle.

(Topologically, take a long prism with a handle on each end, and send a rigid cable once through the hole of each handle.)

@Yemon, new color scheme

When I passed by later, one of the loops was off and the handle was left dangling by the other loop. How is this possible with a continuous transformation on the suitcase handle (and not on the loop comprised of the door and its handle?)

Oh, there are others here now. Caught in the act of mathfitti!

"For every uncountable cardinal and characteristic, there is up to isomorphism one unique field whose size is the given cardinal and whose characteristic is the given one." Is there a name for this proposition, or nice reference (for people who are not big in set theory or model theory)?

@anon I think (but I'm not sure) the Löwenheim-Skolem theorem implies there is at least one field with any given infinite size and any finite characteristic. I don't think you'd get only one model up to isomorphism. For infinite characteristic, I think the proof can be extended, but I'm not sure.

@DavidRoberts The American Discworld books seem to be horrendously ugly.

@anon, a good search term in model theory for this is categoricity. A theorem

related to yours is the categoricity of the theory of algebraically closed fields.

Also the modifier "categorically" is used in such a context. I want to say that "categorical in kappa" or "categorically larger than kappa" is used when models of a theory are isomorphic if they are of a size lambda greater than kappa, but I am unsure of the usage.

heyo