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A general theme of computable structure theory is to investigate when structures have copies of a given complexity $Gamma$. We discuss such problem for the case of equivalence structures and preorders. We show that there is a $Pi^0_1$ equivalence structure with no $Sigma^0_1$ copy, and in fact that the isomorphism types realized by the $Pi^0_1$ equivalence structures coincide with those realized by the $Delta^0_2$ equivalence structures. We also construct a $Sigma^0_1$ preorder with no $Pi^0_1$ copy.
A numbering of a countable family $S$ is a surjective map from the set of natural numbers $omega$ onto $S$. A numbering $ u$ is reducible to a numbering $mu$ if there is an effective procedure which given a $ u$-index of an object from $S$, computes
An $omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $omega$-tree-automatic structures. We prove first that th
While most research in Gold-style learning focuses on learning formal languages, we consider the identification of computable structures, specifically equivalence structures. In our core model the learner gets more and more information about which pa
We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, (relative) $Delta^0_alpha$ bi-embeddable categoricity, and degrees of bi-embeddable catego
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably, invertible terms a