Joint work with Wen Huang, Song Shao and Xiangdong Ye.

We will introduce the model theory of dynamical system. Let $(X,X ,\mu,T)$ be an ergodic dynamical system. We say that $(X',X',\mu',T')$ is a topological model (or just a model) for $(X,X,\mu,T)$ if $(X',T')$ is a topological system, $\mu'$ is an invariant Borel probability measure on $X'$ and the systems $(X,X,\mu,T)$ and $(X',X',\mu',T')$ are measure theoretically isomorphic. We will give a method of constructing a topological model that was created by B. Weiss.