Abstract
We study the index sets of the following properties of computable algebras: to have no nontrivial congruences, to have a finite number of congruences, to have infinite decreasing or increasing chains of congruence relations. We prove completeness of these index sets in arithmetic and hyperarithmetic hierarchies.
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Khoussainov, B., Morozov, A. (2010). On Index Sets of Some Properties of Computable Algebras. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_25
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DOI: https://doi.org/10.1007/978-3-642-13962-8_25
Publisher Name: Springer, Berlin, Heidelberg
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