A Friedberg enumeration of equivalence structures

摘要

We solve a problem posed by Goncharov and Knight (Problem 4 in [S. Goncharov and J. Knight, Computable structure and antistructure theorems, Algebra Logika 41(6) (2002) 639-681, 757 vertical bar). More specifically, we produce an effective Friedberg (i.e. injective) enumeration of computable equivalence structures, up to isomorphism. We also prove that there exists an effective Friedberg enumeration of all isomorphism types of infinite computable equivalence structures.