# Low for omega and equivalence class isomorphism properties

## Jacob Suggs

### University of Connecticut

We look at the property of being low for isomorphism, restricted to certain classes of structures – if *C* is a class of structures, a set *D* is low for *C* isomorphism iff for any two structures in *C*, if *D* computes an isomorphism between them then there is a computable isomorphism between them. In particular we will show that exactly those sets which cannot compute non-zero Δ_{2} degrees are low for ω-isomorphism (when ω is viewed purely as an order), and we will show that no set which computes a non-zero Δ_{2} set or which computes a separating set for any two computably inseparable c.e. degrees is low for equivalence class isomorphism.

Jacob Suggs is a graduate student in computability theory at the University of Connecticut, working with Reed Solomon.