[FOM] Axioms that imply AC

Andrej Bauer 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.

Andrej Bauer

More information about the FOM mailing list