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Mat. Zametki, 2004, Volume 76, Issue 3, Pages 362–371 (Mi mz110)  

This article is cited in 4 scientific papers (total in 4 papers)

Collapse Result for Extensions of the Presburger Arithmetic by a Unary Function Compatible with Addition

S. M. Dudakov

Tver State University

Abstract: Earlier, Belegradek, Stolboushkin, and Taitslin proved that the collapse result holds in the theory of natural numbers with addition, i.e., each locally generic query using addition can be written without it. In this paper, we use the sufficient conditions of the collapse result obtained by Taitslin to prove that it holds in any extensions of the Presburger arithmetic by a unary function compatible with addition. The notion of a function compatible with addition was proposed by A. L. Semenov.

DOI: https://doi.org/10.4213/mzm110

Full text: PDF file (215 kB)
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English version:
Mathematical Notes, 2004, 76:3, 339–347

Bibliographic databases:

UDC: 510.652
Received: 05.02.2002
Revised: 28.08.2003

Citation: S. M. Dudakov, “Collapse Result for Extensions of the Presburger Arithmetic by a Unary Function Compatible with Addition”, Mat. Zametki, 76:3 (2004), 362–371; Math. Notes, 76:3 (2004), 339–347

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm110
  • http://mi.mathnet.ru/eng/mz/v76/i3/p362

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. M. Dudakov, M. A. Taitslin, “Collapse results for query languages in database theory”, Russian Math. Surveys, 61:2 (2006), 195–253  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. S. M. Dudakov, “Pseudofinite Homogeneity, Isolation, and Reducibility”, Math. Notes, 81:4 (2007), 456–466  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. S. M. Dudakov, “Sufficient conditions for effective translation of locally generic queries”, J. Math. Sci., 172:5 (2011), 654–662  mathnet  crossref  mathscinet  elib
    4. S. M. Dudakov, “Monadic structures over an ordered universal random graph and finite automata”, Izv. Math., 75:5 (2011), 915–932  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математические заметки Mathematical Notes
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