Logic Seminar

We consider questions concerning what types of structures can be put in a continuous way on the free actions of Z^n. In particular we consider structures which on each class are finite unions of lines or trees. This is closely related to the continuous automorphism problem which asks on which invariant sets is there a continuous automorphism generating the equivalence relations. The main technical point is a new way of using certain hyperaperiodic elements to get results about continuous structurings. We apply this method to get results about linings, treeings, and some results about the automorphism problem. Parts of the work are joint with C. Olsen and parts with M. Kang.