Reducibilities among equivalence relations induced by recursively enumerable structures

doi:10.1016/j.tcs.2015.11.042

Theoretical Computer Science

Volume 612, 25 January 2016, Pages 137-152

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Abstract

In this paper we investigate the dependence of recursively enumerable structures on the equality relation which is fixed to a specific r.e. equivalence relation. We compare r.e. equivalence relations on the natural numbers with respect to the amount of structures they permit to represent from a given class of structures such as algebras, permutations and linear orders. In particular, we show that for various types of structures represented, there are minimal and maximal elements.

Keywords

Recursively enumerable equivalence classes

Algebraic structures

Reducibilities

Degrees

Realisability

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¹: A. Gavryushkin was partially supported by the FRDF grant of the University of Auckland and by the Federal Target Program “Research and Training Specialists in Innovative Russia, 2009–2013”, Contracts No. Π1227 and No. 16.740.11.0567.

²: The work is partially supported by Marsden Fund of Royal Society New Zealand. B. Khoussainov did part of this work while on Sabbatical Leave to the School of Computing, National University of Singapore.

³: F. Stephan is supported in part by NUS grants R146-000-181-112 and R252-000-420-112.