The field of reals with a predicate for the real algebraic numbers and a predicate for the integer powers of twoMohsen KhaniArch. Math. Log.2015Given a theory TÌƒ of a polynomially bounded expansion RÌƒ of RÌ„ with the field of exponents Q, we introduce a theory T whose models are comprised of a dense pair of models of TÌƒ and a discreteâ€¦ (More)