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

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Grothendieck universe
Posted: May 22, 2013 1:02 AM
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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?

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