This paper deals with the area of problems concerning the discrete systems dynamics and is also related to Wonham's principle of internal model. The authors consider the case of systems with an invariant subsystem and use the improved modelling tool of the theory of topoi. By stressing that the description of a system's evolution (change in time) does not require binary but n‐ary logic, they use the term of dynamic membership and underline the connection between local and global invariance. The fact that binary logic is not enough for modelling discrete systems dynamics reveals once more the representation potential offered by the fuzzy systems theory.