[FOM] Primitive recursive reals

[Harvey Friedman]

On 4/19/06 6:48 PM, "hendrik at topoi.pooq.com" <hendrik at topoi.pooq.com> wrote:

> On Wed, Apr 19, 2006 at 09:38:32AM -0400, Harvey Friedman wrote:
>> 
>> THEOREM 1. Let b1 and b2 be two bases, neither of which is a power of the
>> other. There exists a real number that is (extremely) primitive recursive in
>> base b1 but not primitive recursive in base b2.
> 
> Is the condition on bases quite right?  What if b1 is 4 and b2 is 8?
> 
> -- hendrik boom

You are absolutely right. I have not done this correctly. I think the right
condition is: b2 has a prime factor that does not divide b1.

I am very pressed, and don't have the time now to go into this fully, so I
hope some people take this over for me.

Harvey Friedman