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Topic: Notation
Replies: 14   Last Post: May 27, 2013 1:46 AM

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Posts: 2,720
Registered: 2/15/09
Re: Notation
Posted: May 26, 2013 3:06 PM
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On May 26, 11:25 am, fom <> wrote:
> On 5/25/2013 8:36 PM, William Elliot wrote:

> > On Sat, 25 May 2013, fom wrote:
> >> On 5/24/2013 10:57 PM, William Elliot wrote:
> >>> V is the ZFC universe.
> >>> L is the constructible universe.
> >>> L_omega0 is the omega_0th level of the constructible universe.

> >>> Correct or needing correcting?
> >> Your apparently simple question seems to have generated
> >> some interesting replies.

> > Seemingly off the mark because I'm asking about notation and not about
> > theory.

> Just to clarify something concerning your distinction here,
> let me observe that the sign of equality in "V=L" is
> metamathematical or metalogical or metalinguistic or
> however some purist would like to take it as not being
> part of the "object language".
> In other words, part of the reason your question received
> "theory" replies is because of the class/set distinction
> and its model-theoretic implications.
> These particular notations correspond precisely with
> the point at which philosophy and mathematics (prior
> to intuitionism and categories) meet.  Enough said.

What part of philosophy has non-sets (defined by their elements, i.e.
sets, and non-well-founded, i.e. irregular) for regular set theory,
and collapsible models for extended theory?

That is: why aren't there simply well-founded and non-well-founded
collections in a unified theory? It seems that the Euclidean, for
geometry, can be to the super-Euclidean (Minkowskian), where are sets
to the super-Russellian?

Seems more: too much left unsaid.

And, Russell as to ZF's regular sets (with an _axiomatized_ infinity
of a particular closed _form_ of finitist principles) sees the same
result on the finite sets, for the form. And, if there's a model of
ZF there's an irregular one.


Ross Finlayson

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