[FOM] throwing darts at natural numbers (rejoinder to Arnon Avron's reply)

[Timothy Y. Chow]

On Thu, 6 Aug 2009, joeshipman at aol.com wrote:
> He doesn't need to understand Freiling's proof, he just needs to know the
> statement of Freiling's result, to be able to say "in that case CH sounds
> pretty dubious".

But he could also say, "in that case AC sounds pretty dubious."

> The foundational significance of Freiling's argument is that it is the 
> most counterintuitive consequence of CH yet discovered.

I would call it a consequence of AC + CH rather than a consequence of CH.

> What is the most counterintuitive consequence of not-CH that has been 
> discovered so far?

This is not exactly a "fair fight."  Not-CH by itself is such a weak 
assertion that we don't expect it to have particularly interesting 
consequences on its own.

Tim