Equivalence Relations on Classes of Computable Structures

Abstract. If L is a finite relational language then all computable Lstructures can be effectively enumerated in a sequence {An}n∈ω in such a way that for every computable L-structure B an index n of its isomorphic copy An can be found effectively and uniformly. Having such a universal computable numbering, we can identify computable structures with their indices in this numbering. If K is a class of L-structures closed under isomorphism we denote by Kc the set of all computable members of K. We measure the complexity of a description of Kc or of an equivalence relation on Kc via the complexity of the corresponding sets of indices. If the index set of Kc is hyperarithmetical then (the index sets of) such natural equivalence relations as the isomorphism or bi-embeddability relation are Σ1 1 . In the present paper we study the status of these Σ1 1 equivalence relations (on classes of computable structures with hyperarithmetical index set) within the class of Σ1 1 equivalence rela...

• Type: Conference
• Year: 2009
• Where: CIE
• Authors: Ekaterina B. Fokina, Sy-David Friedman
• Keywords: Applied Computing, CIE 2009, Computable, Computable Structures, Equivalence Relations