On the isomorphism problem for some classes of computable algebraic structures

On the isomorphism problem for some classes of computable algebraic structures Full article

Journal

Archive for Mathematical Logic
ISSN: 0933-5846 , E-ISSN: 1432-0665

Output data

Year: 2022, Volume: 61, Number: 5-6, Pages: 813-825 Pages count : 13 DOI: 10.1007/s00153-021-00811-5

Tags

Computable structure; Distributive lattice; Effective transformation; Isomorphism problem; Nilpotent structure

Authors

Harizanov V.S. ¹ , Lempp S. ² , McCoy C.F.D. ³ , Morozov A.S. ⁴ , Solomon R. ⁵

Affiliations

1	Department of Mathematics, George Washington University, Washington, DC 20052, United States
2	Department of Mathematics, University of Wisconsin, Madison, WI 53706, United States
3	Department of Mathematics, University of Portland, Portland, OR 97203, United States
4	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
5	Department of Mathematics, University of Connecticut, Storrs, CT 06269, United States

We establish that the isomorphism problem for the classes of computable nilpotent rings, distributive lattices, nilpotent groups, and nilpotent semigroups is Σ11-complete, which is as complicated as possible. The method we use is based on uniform effective interpretations of computable binary relations into computable structures from the corresponding algebraic classes.

Harizanov V.S. , Lempp S. , McCoy C.F.D. , Morozov A.S. , Solomon R.
On the isomorphism problem for some classes of computable algebraic structures
Archive for Mathematical Logic. 2022. V.61. N5-6. P.813-825. DOI: 10.1007/s00153-021-00811-5 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000744774600001
Scopus:	2-s2.0-85123257300
Elibrary:	48145047
OpenAlex:	W4206777607

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Scopus	2
Web of science	1
OpenAlex	1
Elibrary	1