Ekaterina B. Fokina

Degrees of categoricity of computable structures

Defining the degree of categoricity of a computable structure

On Σ11 equivalence relations over the natural numbers

{\mathcal{M}}

Linear orders realized by C.e. Equivalence relations

to be the least degree d for which

Classes of structures with universe a subset of ω1

{\mathcal{M}}

Index Sets of Computable Structures with Decidable Theories

is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above 0(n) can be so realized, as can the degree 0(ω).

Isomorphism relations on computable structures

For a computable structure M , the categoricity spectrum is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable copies of M . If the spectrum has a least degree, this degree is called the degree of categoricity of M . In this paper we investigate spectra of categoricity for computable rigid structures. In particular, we give examples of rigid structures without degrees of categoricity.