[FOM] Axioms that imply AC
Andrej.Bauer at andrej.com
Sat Feb 4 17:51:59 EST 2006
On Saturday 04 February 2006 16:48, Timothy Y. Chow wrote:
> What about the generalized continuum hypothesis? Or V = L, or V = OD? Or
> are these not the flavor of statements you're looking for?
I thank everyone for pointing me to the standard references. I was aware of
Rubin's books (which my student is using), but not Felgner. I think I phrased
my question somewhat poorly by writing "or specifically set-theoretic".
I was aware of GCH and of V=L => AC, which as William Tait pointed out goes
via "V is well-ordered". By the way, what is V = OD? (Sorry, I am not a set
theorist. If this is below the threshold for this list, I can look it up
I was rather thinking of statements that carry as little "logical" character
and as much "mathematical" one as possible. For example, is there a "natural"
mathematical theorem which is of the strength "V is well-ordered" that an
"ordinary" mathematician would ever think of? Perhaps something about large
categories, e.g.: if a functor F : C --> D, where C and D may be large
categories, is full, faithful and essentially surjective on objects, then
there exists G : D --> C, such that F and G form an equivalence of
categories. Or even simpler: every category has a skeleton? But these are
rather blatant uses of "big choice". I hoped for something subtler than that.
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