[FOM] Countable choice

Bill Taylor W.Taylor at math.canterbury.ac.nz
Sun Jun 15 23:12:22 EDT 2008

Robert Black <Mongre at gmx.de> chastises me:

->>-> sets - anything to do with possible constructions in time?

->> Of course it is not a matter of "time", as in physical time,
->> but a matter of necessary logical priority, which is all to do with omega.

My apologies, I got crossed wires here.  

I meant "all to do with well-ordering", as you noted later was
the essential point of the Scott paper.

(My remarks on omega were me getting confused with the existence of PROOFS.
 THAT is what is "all to do with omega".   Again, sorry.)
-> The intuition supporting 
-> the cumulative hierarchy is that sets presuppose their members 
-> I would prefer to say metaphysically rather than logically,

Yes, that is probably a better thing to say.

So anyway, my original comment should have been, sets have everything
to do with well-ordering by membership.  OC, there *are* set theories
(like Aczel's) that reject this; but IMHO they are not really set
theories, but a disguised form of graph theory.

-- Bill Taylor

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