For example, let R be the ordered field of real algebraic numbers with the usual ordering < inherited from R.  Take a transcendental number, say π, and add a unary relation S to the structure given by the subset (−π,π) ∩ R.  Now consider the subset A of R defined by the formula
Let R be an ordered field of real algebraic numbers, inheriting the usual ordering < from R. Choose a transcendental number, such as π, and introduce a unary relation S to the structure formed by the subset (−π,π) ∩ R. Consider the subset A in R defined by the formula.