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Chebyshevskii Sbornik, 2020, Volume 21, Issue 4, Pages 56–71
DOI: https://doi.org/10.22405/2226-8383-2018-21-4-56-71 (Mi cheb952) 		 
On “simple” algorithmically undecidable fragments of elementary theory of an infinitely generated free semigroup

V. G. Durnev, O. V. Zetkina, A. I. Zetkina

P. G. Demidov Yaroslavl' University (Yaroslavl')
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DOI: https://doi.org/10.22405/2226-8383-2018-21-4-56-71
Abstract: We prove algorithmic undecidability of $\exists \forall^2 \exists^3$-theory for a free semigroup of countable rank. This strengthens the classical Quine's (1946) result [1] on algorithmic undecidability of elementary theory of an arbitrary non-cyclic free semigroup.
Keywords: free semigroups, elementary theories.
Received: 24.04.2020
Accepted: 22.10.2020
Document Type: Article
UDC: 512+512.5+512.54+512.54.03
Language: Russian
Citation: V. G. Durnev, O. V. Zetkina, A. I. Zetkina, “On “simple” algorithmically undecidable fragments of elementary theory of an infinitely generated free semigroup”, Chebyshevskii Sb., 21:4 (2020), 56–71
Citation in format AMSBIB
\Bibitem{DurZetZet20}
\by V.~G.~Durnev, O.~V.~Zetkina, A.~I.~Zetkina
\paper On ``simple'' algorithmically undecidable fragments of elementary theory of an infinitely generated free semigroup
\jour Chebyshevskii Sb.
\yr 2020
\vol 21
\issue 4
\pages 56--71
\mathnet{http://mi.mathnet.ru/cheb952}
\crossref{https://doi.org/10.22405/2226-8383-2018-21-4-56-71}
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