Leo Harrington Department of Mathematics University of California, Berkeley Berkeley, CA 94720, leo@math.berkeley.edu Title: Invariant Jump Classes (Special Session on Computability Theory) This talk will report on joint work with Peter Cholak. A class of r.e. sets is called invariant with respect to the structure of all r.e. sets if it is fixed by all automorphisms of that structure. A class of Turing degrees of r.e. sets is called invariant if it is the class of degrees of members of an invariant set. It is shown that for n > 1, the high-n classes and the complements of the low-n classes are all invariant.