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.