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arXiv · 2001.08017

Comparing the isomorphism types of equivalence structures and preorders

Nikolay Bazhenov·Luca San Mauro
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Abstract

A general theme of computable structure theory is to investigate when structures have copies of a given complexity $Γ$. We discuss such problem for the case of equivalence structures and preorders. We show that there is a $Π^0_1$ equivalence structure with no $Σ^0_1$ copy, and in fact that the isomorphism types realized by the $Π^0_1$ equivalence structures coincide with those realized by the $Δ^0_2$ equivalence structures. We also construct a $Σ^0_1$ preorder with no $Π^0_1$ copy.

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Nikolay Bazhenov, Luca San Mauro. 2020-01-22. Comparing the isomorphism types of equivalence structures and preorders. https://arxiv.org/abs/2001.08017

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