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Izvestiya: Mathematics, 2004, Volume 68, Issue 5, Pages 911–933
DOI: https://doi.org/10.1070/IM2004v068n05ABEH000503
(Mi im503)
 

This article is cited in 6 scientific papers (total in 6 papers)

The collapse theorem for theories of $I$-reducible algebraic systems

S. M. Dudakov

Tver State University
References:
Abstract: We study $I$-reducible algebraic systems and the theory of $I$-reducible systems. We show that the lack of an independent formula in a theory is not a necessary condition for the $I$-reducibility of its models, even for extensions of Presburger arithmetic. In particular, there is an entire class of theories that are extensions of Presburger arithmetic in which there is an independent formula and which have $I$-reducible models. We show that the $I$-reducibility of a small algebraic systems automatically implies that every formula is equivalent in it to a $P$-restricted formula, and thus the collapse theorem holds for the theories of such systems.
Received: 18.02.2003
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2004, Volume 68, Issue 5, Pages 67–90
DOI: https://doi.org/10.4213/im503
Bibliographic databases:
UDC: 510.652
MSC: 03C65, 08A70, 68P15
Language: English
Original paper language: Russian
Citation: S. M. Dudakov, “The collapse theorem for theories of $I$-reducible algebraic systems”, Izv. RAN. Ser. Mat., 68:5 (2004), 67–90; Izv. Math., 68:5 (2004), 911–933
Citation in format AMSBIB
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\by S.~M.~Dudakov
\paper The collapse theorem for theories of $I$-reducible algebraic systems
\jour Izv. RAN. Ser. Mat.
\yr 2004
\vol 68
\issue 5
\pages 67--90
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\zmath{https://zbmath.org/?q=an:1080.03021}
\transl
\jour Izv. Math.
\yr 2004
\vol 68
\issue 5
\pages 911--933
\crossref{https://doi.org/10.1070/IM2004v068n05ABEH000503}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746516809}
Linking options:
  • https://www.mathnet.ru/eng/im503
  • https://doi.org/10.1070/IM2004v068n05ABEH000503
  • https://www.mathnet.ru/eng/im/v68/i5/p67
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:443
    Russian version PDF:185
    English version PDF:8
    References:49
    First page:1
     
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