Every well-order structure, for example, is necessarily rigid, but when an order is sufficiently large—larger than the continuum is enough—then not every point can be characterized by its properties, simply because there aren’t enough sets of formulas in the language to distinguish all the points, and so it will not be Leibnizian. Indeed, for any language ℒ, every sufficiently large ℒ-structure will fail to be Leibnizian for the same reason.
