Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic

For every sequence |p_n}_n of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory diagonalizable algebras, we associate a formula⁰A, called the value ofA inPA with respect to the interpretation.We show that, ifA is true in every diagonalizable algebra, then, for every, ⁰A is a theorem ofPA.