| Résume | Continuous logic is a multi-valued logic developed in the recent years to study metric structures. In the classical logic, Urysohn in 1925 proved the existence of a separable universal ultrahomogeneous metric space, which is now known as the Urysohn space. We consider the problem whether similar Urysohn structures exist in continuous logic. It turns out that the answer depends on the property of the signature of the logic. In this talk I will give a complete characterization of when such Urysohn structures exist, and further discuss the properties of the Urysohn structures when they exist. This is joint work with Wei Dai, Xuanzhi Ren, and Victor Hugo Yanez. |
