Abstract: A subset in the ideal boundary of a CAT(0) space is called symmetric if every complete geodesic with one ideal boundary point in the set has both ideal boundary points in the set. In the late 80s Eberlein proved that if a Hadamard manifold contains a non-trivial closed symmetric subset in its ideal boundary, then its holonomy group cannot act transitively. This leads to rigidty via the Berger-Simons Theorem. I will discuss rigidity of ideal symmetric sets in the general context of locally compact geodesically complete CAT(0) spaces.