STRUCTURAL HIGHNESS NOTIONS
Wesley Calvert, Johanna N. Y. Franklin, Dan Turetsky · Journal of Symbolic Logic · 2022
Abstract We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and several other problems related to computing isomorphisms. These other problems include Scott analysis (in the form of back-and-forth relations), jump hierarchies, and computing descending sequences in linear orders.