[FOM] Infinity Axiom

Thomas Forster T.Forster at dpmms.cam.ac.uk
Mon Jul 21 18:08:52 EDT 2008


This is discussed in some detail in a recent article by Mathias in the 
JSL, entitled (i think) *Slim Models of Zermelo set theory* and i think 
you will find in it suitable pointers to the original literature.   It is 
also covered in my forthcoming pamphlet *An Introduction to the axioms of 
set theory* soon to be brought out by Cambridge university press.

         v best wishes


On Sun, 20 Jul 2008, Harvey 
Friedman wrote:

> It is well known that
> 1. ZF with the usual axiom of infinity - having emptyset and closed  
> under x goes to x union {x} - proves the existence of V(omega); yet
> 2. Zermelo, even with choice and foundation, with the usual axiom of  
> infinity, does not prove the existence of V(omega).
> However, I don't know what reference should be used for this, or how  
> credit should be assigned.
> Can anyone help?
> Harvey Friedman
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