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Embedding of the Atomic Theory of Subsets of Free Semigroups to the Atomic Theory of Subsets of Free Monoids

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Abstract

In this paper, atomic formulas are considered that are 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, \(Y\backslash X\) (multiplying on the left) is defined. 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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Authors and Affiliations

  1. Chair of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    B. O. Konstantinovskiy & F. D. Kholodilov

Authors
  1. B. O. Konstantinovskiy
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  2. F. D. Kholodilov
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Correspondence to B. O. Konstantinovskiy or F. D. Kholodilov.

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The authors declare that they have no conflicts of interest.

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Translated by E. Oborin

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Konstantinovskiy, B.O., Kholodilov, F.D. Embedding of the Atomic Theory of Subsets of Free Semigroups to the Atomic Theory of Subsets of Free Monoids. Moscow Univ. Math. Bull. 77, 108–111 (2022). https://doi.org/10.3103/S002713222202005X

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