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Matematicheskie Zametki, 2004, Volume 76, Issue 3, Pages 362–371
DOI: https://doi.org/10.4213/mzm110 (Mi mzm110) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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

S. M. Dudakov

Tver State University
Full-text PDF (215 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm110
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.
Received: 05.02.2002
Revised: 28.08.2003
English version:
Mathematical Notes, 2004, Volume 76, Issue 3, Pages 339–347
DOI: https://doi.org/10.1023/B:MATN.0000043461.68759.1d
Bibliographic databases:
UDC: 510.652
Language: Russian
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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\pages 362--371
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  • https://www.mathnet.ru/eng/mzm110
  • https://doi.org/10.4213/mzm110
  • https://www.mathnet.ru/eng/mzm/v76/i3/p362
    • This publication is cited in the following 5 articles:
    1. Sergey M. Dudakov, “On inflationary fix-point operators safety”, Lobachevskii J Math, 36:4 (2015), 328  crossref
    2. 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
    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, “Pseudofinite Homogeneity, Isolation, and Reducibility”, Math. Notes, 81:4 (2007), 456–466  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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