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 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.