[FOM] Eliminating AC

[Craig Smorynski]

Maybe you can wave your hands with "hereditarily ordinally definable sets" and point out that ordinal definability makes every set well-orderable (whence AC is true) and the set of natural numbers is in HOD.

On Mar 21, 2013, at 1:47 PM, Joe Shipman wrote:

> I am looking for something that I can explain in a few minutes to a mathematician who is unfamiliar with Godel constructibility, so that he will feel he understands why the result is true.
> 
> -- JS
> 
> Sent from my iPhone
> 
> On Mar 21, 2013, at 12:17 AM, Craig Smorynski <smorynski at sbcglobal.net> wrote:
> 
> The original proof by noticing that the natural numbers in V and L are the same must surely be as simple as possible, which of course is not to say that it is simple.
> 
> On Mar 20, 2013, at 7:52 PM, Joe Shipman wrote:
> 
>> What is the simplest way to see that any arithmetical consequence of ZFC is a consequence of ZF?
>> 
>> -- JS
>> _______________________________________________
>> FOM mailing list
>> FOM at cs.nyu.edu
>> http://www.cs.nyu.edu/mailman/listinfo/fom
> 
> Craig
> 
> 
> 
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom

Craig



-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20130321/ebde152b/attachment.html>