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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 274, Pages 291–296 (Mi tm3315)  

This article is cited in 2 scientific papers (total in 2 papers)

Finite quantifier hierarchies in relational algebras

A. L. Semenov, S. F. Soprunov

Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (151 kB) Citations (2)
References:
Abstract: For a given structure of finite signature, one can construct a hierarchy of classes of relations definable in this structure according to the number of quantifier alternations in the formulas expressing the relations. In ordinary examples, this hierarchy is either infinite (as in the arithmetic of addition and multiplication of natural numbers) or stabilizes very rapidly (in structures with decidable theories, such as the field of real numbers). In the present paper, we construct a series of examples showing that the above-mentioned hierarchy may have an arbitrary finite length. The proof employs a modification of the Ehrenfeucht game.
Received in December 2010
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 274, Pages 267–272
DOI: https://doi.org/10.1134/S0081543811060162
Bibliographic databases:
Document Type: Article
UDC: 510.635
Language: Russian
Citation: A. L. Semenov, S. F. Soprunov, “Finite quantifier hierarchies in relational algebras”, Algorithmic aspects of algebra and logic, Collected papers. Dedicated to Academician Sergei Ivanovich Adian on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 274, MAIK Nauka/Interperiodica, Moscow, 2011, 291–296; Proc. Steklov Inst. Math., 274 (2011), 267–272
Citation in format AMSBIB
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\pages 291--296
\publ MAIK Nauka/Interperiodica
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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