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Identical inclusions of semilattices

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Abstract

The class of identical inclusions was defined by Lyapin. We prove that any set of identical inclusions in the class of semilattices is equivalent to an elementary (the first order) formula. Elementary identical inclusions forms the class of universal formulas which is situated strictly between identities and universal positive formulas. We describe the infinite lattice of all classes of semilattices which can be defined by sets of identical inclusions and solve the main algorithmic problems concerning identical inclusions of semilattices.

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Acknowledgements

The author is grateful to Boris M. Schein for numerous discussions that contribute to the essential improvement of the design of the paper.

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  1. Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva, Israel

    G. Mashevitzky

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  1. G. Mashevitzky
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Correspondence to G. Mashevitzky.

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Presented by Edmond W. H. Lee.

Dedicated to Professor Evgeny Sergeevich Lyapin.

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Mashevitzky, G. Identical inclusions of semilattices. Algebra Univers. 81, 26 (2020). https://doi.org/10.1007/s00012-020-0649-6

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