> Similar comments apply, less strongly, to similar > independence results in point-set topology (in my opinion; some > people who style themselves "point-set topologists" look--to the > extent that there are still any of them on the hoof--like straight > out "logicians with an interest in pathology" to most other topologists).
Point set topology has always had a pathology lab attached to it. What's happened I think is that a somewhat moribund subject has been revitalized; set theoric topology turning in to the place where the action is. The theory of abelian groups is somewhat similar--a category with a rather simple structure, which gets livened up by set theory. It makes sense if you look at the category with all functions as its morphisms--namely, sets--by way of comparison.
> >Cabal-type intutions, that the continuum hypothesis is false and > >Martin's axiom true, lead to one answer, whereas the minimalist > >hypothesis that all sets are constructible leads to another. You get > >the exact same division over Suslin lines; there are two very different > >flavors of set theory extensions which these reflect. > > And yet life goes on. Amazingly.
What if you wanted to tie a knot in a Suslin line? It would help if they existed.