I have to find two interpretation so that a formula alpha is $$ \Im1(\alpha)=0$$ $$\Im 2(\alpha)=1$$ in $$\mathbb N$$ The given formulas are:
$$ \alpha1 = \forall x \forall y \forall z \forall u ((P(u,x) \land Q(x,y,z)) \to P(u,z)) $$ $$ \alpha2 = \forall x \forall y (P(x,y) \land P(f(x),f(y)) \to P(x,f(x)) \land P(y,f(y))) $$
i dont know how i can find interpretations so that the formulas are $$ \Im1(\alpha)=0$$ $$\Im 2(\alpha)=1$$