On finite subsets monoid with decidable theory
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2024), pp. 27-38
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In our previous works, we have proved for various associative algebras that the finite subsets theory allows to interpret elementary arithmetic, in particular, such theory is undecidable. For example, this is proved for all infinite Abelian groups. A natural question arises: can we generalize this result to a wider class of algebras, for example, all commutative monoids. In some cases, we also have proved analogous result: for commutative cancellative monoids with an element of infinite order, or arbitrary Abelian groups. In this paper we prove that this is not true for arbitrary commutative monoids. Moreover, we propose a method that allows to construct such algebras by various original algebras. Also, we have found a limitation of this method.
Keywords:
subset algebra, algorithmic decidability, automatic structure.
@article{VTPMK_2024_2_a2,
author = {S. M. Dudakov},
title = {On finite subsets monoid with decidable theory},
journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
pages = {27--38},
publisher = {mathdoc},
number = {2},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTPMK_2024_2_a2/}
}
S. M. Dudakov. On finite subsets monoid with decidable theory. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2024), pp. 27-38. http://geodesic.mathdoc.fr/item/VTPMK_2024_2_a2/