
Re: Notation
Posted:
May 26, 2013 3:06 PM


On May 26, 11:25 am, fom <fomJ...@nyms.net> 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 modeltheoretic 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 nonsets (defined by their elements, i.e. sets, and nonwellfounded, i.e. irregular) for regular set theory, and collapsible models for extended theory?
That is: why aren't there simply wellfounded and nonwellfounded collections in a unified theory? It seems that the Euclidean, for geometry, can be to the superEuclidean (Minkowskian), where are sets to the superRussellian?
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.
Regards,
Ross Finlayson

