Geodesic
Embedding of the atomic theory of subsets of free semigroups to the atomic theory of subsets of free monoids
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2022), pp. 76-79 
B. O. Konstantinovskiy; F. D. Kholodilov. Embedding of the atomic theory of subsets of free semigroups to the atomic theory of subsets of free monoids. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2022), pp. 76-79. http://geodesic.mathdoc.fr/item/VMUMM_2022_2_a12/
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     author = {B. O. Konstantinovskiy and F. D. Kholodilov},
     title = {Embedding of the atomic theory of subsets of free semigroups to the atomic theory of subsets of free monoids},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {76--79},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_2_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider atomic formulas constructed from the binary predicate symbol $\subseteq$ and binary function symbols $\backslash$, $/$, $\cup$, and $\cap$. For $X$ and $Y$ from the powerset of a free semigroup, $X/Y$ denotes the set consisting of elements whose product with any element of $Y$ ( multiplying on the right) belongs to $X$. Similarly, one defines $Y \backslash X$ (multiplying on the left). We prove that every atomic formula that is true in every free semigroup powerset interpretation is also true in every free monoid powerset interpretation.

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