[FOM] throwing darts at natural numbers (rejoinder to Arnon Avron's reply)
Timothy Y. Chow
tchow at alum.mit.edu
Thu Aug 6 13:10:26 EDT 2009
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.
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