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Relative universality and universality obtained by adding constants

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A variety \({\mathbb{V}}\) is var-relatively universal if it contains a subvariety \({\mathbb{W}}\) such that the class of all homomorphisms that do not factorize through any algebra in \({\mathbb{W}}\) is algebraically universal. And \({\mathbb{V}}\) has an algebraically universal α-expansion \({\alpha\mathbb{V}}\) if adding α nullary operations to all algebras in \({\mathbb{V}}\) gives rise to a class \({\alpha\mathbb{V}}\) of algebras that is algebraically universal. The first two authors have conjectured that any varrelative universal variety \({\mathbb{V}}\) has an algebraically universal α-expansion \({\alpha\mathbb{V}}\) . This note contains a more general result that proves this conjecture.

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Correspondence to Jiří Sichler.

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Presented by V. Trnková.

The first author acknowledges the support of the project MSM6840770038 of the Czech Ministry of Education. The second author acknowledges the support of the project 1M0022162080 of the Czech Ministry of Education. Financial support of the NSERC of Canada is gratefully acknowledged by the second and third authors.

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Demlová, M., Koubek, V. & Sichler, J. Relative universality and universality obtained by adding constants. Algebra Univers. 65, 179–184 (2011). https://doi.org/10.1007/s00012-011-0122-7

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  • DOI: https://doi.org/10.1007/s00012-011-0122-7

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