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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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