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\(\Delta^0_2\)-categoricity of equivalence structures. (English) Zbl 1234.03021
Summary: We exhibit computable equivalence structures, one \(\Delta^0_2\)-categorical and one not \(\Delta^0_2\)-categorical, having unbounded character, infinitely many infinite equivalence classes, and no \(s_{1}\)-function. This offers a natural example where \(\Delta^0_2\)-categoricity and relative \(\Delta^0_2\)-categoricity differ.

MSC:
03C57 Computable structure theory, computable model theory
03C35 Categoricity and completeness of theories
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