[FOM] Infinity Axiom

[Harvey Friedman]

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