Exercise: Set up a FOL L for Arithmatic in the natural numbers, and using the standard interpretation to express that n is prime number.

Solution: Because the nonlogical symbols defines the first order language. We define the arithmatic in the natural numbers as following:

Functions: +, *;

Relations: <

Constant: 0, 1.

to express n is prime number, we have following formula:

V(m<n & 1<n), k*m = n

Interpretation to express n is prime number: