Another Interpretation

Let W = (forall x) (P(a) & Q(x, a) )

An interpretation for W:

D = { 0, 1, 2, . . . }

{ a = 0 } mapping for constants

{ } mappings for functions

{ P(n) iff n = 0; mappings for predicates

Q(m,n) iff n > m. }

Note that ~Q(x, x).

This interpretation fails to satisfy W. It’s not a model for W.