4 research outputs found
Isomorphism relations on computable structures
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The hierarchy of equivalence relations on the natural numbers under computable reducibility
The notion of computable reducibility between equivalence relations on the
natural numbers provides a natural computable analogue of Borel reducibility.
We investigate the computable reducibility hierarchy, comparing and contrasting
it with the Borel reducibility hierarchy from descriptive set theory.
Meanwhile, the notion of computable reducibility appears well suited for an
analysis of equivalence relations on the c.e.\ sets, and more specifically, on
various classes of c.e.\ structures. This is a rich context with many natural
examples, such as the isomorphism relation on c.e.\ graphs or on computably
presented groups. Here, our exposition extends earlier work in the literature
concerning the classification of computable structures. An abundance of open
questions remains.Comment: To appear in Computabilit