William Tait wwtx at earthlink.net
Sun Mar 12 12:02:18 EST 2006

> I need help with the following.
> Torkel Franzen introduces (in Inexhaustibility pp.156-162) a set O  
> of arithmetized notations for ordinals below omega-1-CK.
> On page 189 he writes that by Kleene's second recursion theorem (p.  
> 155) there is a function index e such that:
> 1. {e}(0) = suc(lim(e))
> where “{e}(0)” and “suc(lim(e))” are numbers/notations in O (p.157)  
> and {e} denotes the function whose index is e.

The second recursion theorem does not yield that {e} is even a total  
function, much less that lim(e) is in O.

Best regards,

Bill Tait

More information about the FOM mailing list