[FOM] Status of AC
Andrej.Bauer at andrej.com
Wed Mar 1 02:29:56 EST 2006
On Tuesday 28 February 2006 09:28, Dung Nguyen wrote:
> To me, it seems quite unthinkable to drop AC, since without it a large part
> of mathematics would collapse (e.g. can anyone think of model theory
> without Compactness or topology without Tychonoff?).
I would be one of those people who think of topology without (general)
Tychonoff, thank you very much. It's very interesting and conceptually
pleasing. Also, it might be interesting for you to have a look at Peter
Johnstone's "Stone spaces" (Theorem III.1.7) for a proof of Tychonoff for
locales without axiom of choice.
It is false that "mathematics collapses" without the axiom of choice, although
a little choice comes in very handy.
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