[FOM] Use of AC

Thomas Forster T.Forster at dpmms.cam.ac.uk
Sun Aug 16 18:18:44 EDT 2009


     No offence taken either.  I am preparing the final version 
of an Introduction to the Axioms of Set Theory that contains a 
chapter that is precisely the 20--30-page treatment of AC that 
you seek.  (At least, that's what it's intended to be!!)  It's 
on www.dpmms.cam.ac.uk/~tf/axiomsofsettheory.pdf. I'm sending it 
off to Cambridge University Press in the next few weeks. Comments 
from listmembers welcome

On Sat, 15 Aug 
2009, Gergely Buday wrote:

> 2009/8/10 Thomas Forster <T.Forster at dpmms.cam.ac.uk>:
> > This is spiralling out of control, so this will be my last post. Implicit
> > use of AC is everywhere, of course.  What is not everywhere is the kind of
> > understanding of AC that FOM listmembers have. Arnon's illustration is a
> > good one.  I ask: how many of the people who learn this fact as u/gs can
> > identify and explain the use of DC in its proof?  Precious few, i bet.
> There might be a problem with textbooks. What I see is that either
> they are too technical for a broader audience and deal with
> specialists' material or cover the question very shallowly (yes, even
> yours, pp. 205-208 in Logic, Induction and Sets, no offense meant). I
> said "what I see" - is there a 20-30 pages introduction to the subject
> that is readable for the non-specialist?
> - Gergely
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