Geodesic
On theory of finite subsets monoid for one torsion abelian group
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 39-55

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Earlier it was proved the following claim. Let G be a non-torsion abelian group and G be the semigroup of finite subsets of G. Then elementary arithmetic can be interpreted in $G^*$, so the theory of $G^*$ is undecidable. Here we prove the same result for one torsion group, the multiplicative group of all roots of unity.
Mots-clés : torsion group
Keywords: semigroup of subsets, elementary arithmetic, undecidability. 
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     author = {S. M. Dudakov},
     title = {On theory of finite subsets monoid for one torsion abelian group},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {39--55},
     publisher = {mathdoc},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a3/}
}
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S. M. Dudakov. On theory of finite subsets monoid for one torsion abelian group. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 39-55. http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a3/