I want to express the following sentence in first order logic.

There are naturals numbers that can not be expressed as one natural number raised to the power of another natural number other than one.

Under normal circumstances this is very simple. I am wondering if the the exponent function involved here can be expressed as uninterpreted function. Can we use some combination of *,+ as interpreted functions to express exponent function as uninterpreted one ?

somefixing of interpretations to be able to make your language describe exponentiation: what do you have in mind? – Charles Stewart Aug 11 '10 at 9:49