[FOM] Paul Cohen was wrong

[T.Forster at dpmms.cam.ac.uk]

On Sep 12 2011, Daniel Mehkeri wrote:

>You could just as well say dependent choice is just a special case of 
>choice. But they are not obviously in the same spirit. (Especially if 
>you are a constructivist.)

There have been people who say that countable choice is a separate 
principle from full AC, and not merely a special case of it. I have on my 
laptop a .pdf file of a paper by Peter Schuster entitled `Countable Choice 
as a questionable Uniformity principle' which i was sent by the author. I 
cannot for the moment recall where it appeared. I think part of this view 
is that countable choice is the principle that supertasks of certain kinds 
can be performed.

I am attracted by both these theses: (i) that the principle that every 
aleph has a successor is not just a consequence of the power set axiom but 
is a separate principle, and (ii) the thought that countable choice is a 
different principle from AC that just happens to be a special case of it.