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 Tr. Mat. Inst. Steklova, 2003, Volume 242, Pages 103–107 (Mi tm408)

Finiteness Conditions for Algebras of Relations

A. L. Semenov

Institute of New Technologies

Abstract: Algebras of relations on a given set are considered; operations in an algebra are specified by various formulas of first-order logic. Different ways of introducing finiteness conditions for such algebras are studied. For each natural $n$, an example of an algebra is constructed that is generated by one $n$-ary relation and cannot be generated by its relations of smaller arity. An open problem is formulated.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2003, 242, 92–96

Bibliographic databases:
UDC: 510.53+510.6

Citation: A. L. Semenov, “Finiteness Conditions for Algebras of Relations”, Mathematical logic and algebra, Collected papers. Dedicated to the 100th birthday of academician Petr Sergeevich Novikov, Tr. Mat. Inst. Steklova, 242, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 103–107; Proc. Steklov Inst. Math., 242 (2003), 92–96

Citation in format AMSBIB
\Bibitem{Sem03} \by A.~L.~Semenov \paper Finiteness Conditions for Algebras of Relations \inbook Mathematical logic and algebra \bookinfo Collected papers. Dedicated to the 100th birthday of academician Petr Sergeevich Novikov \serial Tr. Mat. Inst. Steklova \yr 2003 \vol 242 \pages 103--107 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm408} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2054488} \zmath{https://zbmath.org/?q=an:1079.03063} \transl \jour Proc. Steklov Inst. Math. \yr 2003 \vol 242 \pages 92--96 

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This publication is cited in the following articles:
1. A. L. Semenov, S. F. Soprunov, “Finite quantifier hierarchies in relational algebras”, Proc. Steklov Inst. Math., 274 (2011), 267–272
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