08/30/2012, 05:24 PM

Well. The reason I ask is because I was structuring my semi operators around the distribution of the set:

claim that there are operators unique to x and y which allow us to perform operations on elements of instead of operations on . We then say that is an isomorphism from

Then I found out I only needed to prove the recursive identity for primitive elements of ; (i.e elements that return primes in N); and then do the rest by induction and breaking up the real argument into a product of primitive elements.

However; this all and all sounded plausible but I hit some huge wall. Which is proving the recursive identity for primitive elements; mostly.

I have a new technique now. It may or may not work.

But having more information about how behaves for naturals would really help.

claim that there are operators unique to x and y which allow us to perform operations on elements of instead of operations on . We then say that is an isomorphism from

Then I found out I only needed to prove the recursive identity for primitive elements of ; (i.e elements that return primes in N); and then do the rest by induction and breaking up the real argument into a product of primitive elements.

However; this all and all sounded plausible but I hit some huge wall. Which is proving the recursive identity for primitive elements; mostly.

I have a new technique now. It may or may not work.

But having more information about how behaves for naturals would really help.