Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Grothendieck universe
Replies: 5   Last Post: May 22, 2013 5:41 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 1,230
Registered: 1/8/12
Re: Grothendieck universe
Posted: May 22, 2013 1:02 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Tue, 21 May 2013, fom wrote:
> > > There are two simple universes discussed (empty set
> > > and V_omega). The rest are associated with the
> > > existence of strongly inaccessible cardinals.

> >
> > The latter don't exist in ZFO. So V_omega0 is the only
> > non-trivial Grothendeick universe. Doesn't |V_omega0| = aleph_omega0

>
> I believe this is correct.
>

> > which is almost always big enough for mathematics?
> >

>
> Well, that depends on what you mean by "mathematics".
>
> I wrote a set theory that includes a universal class.
> I believe it is minimally modeled by an inaccessible
> cardinal (when the axiom of infinity is included). My
> argument for such a structure is that the philosophy
> of mathematics ought to be responsible for the ontology
> of its objects. So, I reject predicativist views that
> take "numbers" as given.
>
> My views, however, are non-standard and I am still working
> at how to understand them in relation to standard paradigms.


I'm a bearded prochoice mathematican who shaves with Occams
razor. Thus ZFO, ZF + Occams razor proves GCH, hence AxC
and no inaccessibles. I've yet to determine if ZFO proves
V = L. Perhaps it does.

How does ZFO jib with your views?




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.