Original:  In predicate logic, if P is a predicate  over the natural numbers, it is expressed as : That is, if P is decidable, and it cannot be false for every natural number n, then it is true for somen .
Revised:  In predicate logic, if P is a predicate over the natural numbers, it is expressed as : That is, if P is decidable, and it cannot be false for all natural numbers n, then it is true for somen .
Edit intent: clarity