The classical Tarski theorem on topological semantics of modal logic states that the logic S4 is complete in R for each n. Recently several authors have considered logics of dynamic topological systems, which is a topological space and a function on it. In [1] a bimodal logic S4C was introduced and proven to be complete with respect to the class of all continuous dynamic systems. A number of po...

For a compact metric space X let G = H(X) denote the group of self homeomorphisms with the topology of uniform convergence. The group G acts on itself by conjugation and we say that X satisfies the topological Rohlin property if this action has dense orbits. We show that the Hilbert cube, the Cantor set and, with a slight modification, also even dimensional spheres, satisfy this property. We al...