Strong Degrees of Categoricity and Weak Density

© 2020, Pleiades Publishing, Ltd. Abstract: It is well-known that every c.e. Turing degree is the degree of categoricity of a rigid structure. In this work we study the possibility of extension of this result to properly 2-c.e. degrees. We found a condition such that if a Δ02-degree is a degree of categoricity of a rigid structure and satisfies this condition then it must be c.e. Also we show that degrees of non-categoricity are dense in the c.e. degrees