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 with the usual ordering < inherited from R. Pick a transcendental number, such as π, and incorporate a unary relation S into the structure that encompasses the subset (−π,π) ∩ R. Analyze the subset A in R defined by this formula.