Abstract
For many-sorted algebras, Garrett Birkhoff’s characterization of equational classes is proved to generalize in case of finitely many sorts. For infinitely sorted algebras, closure under directed unions needs to be added.
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Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories. Cambridge University Press (1994)
Adámek, J., Rosický, J., Vitale, E.M.: Algebraic Theories. Cambridge University Press (2011)
Birkhoff G.: On the structure of abstract algebras. Proc. Camb. Philos. Soc. 31, 433–454 (1935)
Ehrig, H.-D., Mahr, B.: Fundamentals of Algebraic Specifications 1. Springer (1985)
Loecks, J., Ehrig, H.-D., Wolf, M.: Specification of Abstract Data Types. Wiley and Teubner (1996)
Wechler, W.: Universal Algebra for Computer Scientists. Springer (1992)
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Presented by H.P. Gumm.
The research of the second author was supported by the Ministry of Education of the Czech Republic under the project 1M0545. The research of the third author was supported by FNRS grant 1.5.276.09.
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Adámek, J., Rosický, J. & Vitale, E.M. Birkhoff’s variety theorem in many sorts. Algebra Univers. 68, 39–42 (2012). https://doi.org/10.1007/s00012-012-0185-0
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DOI: https://doi.org/10.1007/s00012-012-0185-0