🚀 go-pugleaf

wft@math.canterbury.ac.nz writes:

Some conception of the
iterative hierarchy seems unavoidable as the intended model of ZF, which in
turn seems unimpeachable as formalizing the basic Cantorian ideas.

All the same, I have a lingering sympathy with Gudeman's objection that
this has not yet perhaps been *completely* demonstrated, and that there may
still be some way of approaching set theory less restrictively than size
limitation or the iterative hierarchy. I should say I think it exceptionally
*unlikely* that any such approach will be found, (as do most mathematicans),
but it seems to me the possibility cannot yet be totally dismissed.



I write:

What about Aczel's AFA?  I don't think there's any profound difficulty
pointed up by Russell's paradox, no more so than in trying to solve
x=x+1.  Aczel has shown that there's a very nice, natural set theory