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Uspekhi Mat. Nauk, 2006, Volume 61, Issue 2(368), Pages 3–66 (Mi umn1713)  

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

Collapse results for query languages in database theory

S. M. Dudakov, M. A. Taitslin

Tver State University

Abstract: This is a survey of collapse results obtained mainly by members of the Tver State University seminar on the theoretical foundations of computer science. Attention is focused on the relative properties of isolation and pseudo-finite homogeneity and universes without the independence property. The Baldwin–Benedikt reducibility theorem is proved for these universes. The Dudakov boundedness theorem is proved for reducible theories. The relative isolation theorem is proved for reducible and bounded theories, and as a consequence the collapse theorem is obtained for reducible theories. It is noted that reducibility is equivalent to the relative property of isolation. On the other hand, results of Dudakov are presented showing that the effectively reducible theories having an effective almost indiscernible sequence admit an effective collapse of locally generic queries using not only ordering and titles of stored tables but also relations and operations in the universe, into queries not using relations and operations in the universe. Also presented is Dudakov's example of an enrichment of the Presburger arithmetic for which the collapse theorem fails but the elementary theory of the enrichment is decidable. This answers some open questions in the negative.

DOI: https://doi.org/10.4213/rm1713

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English version:
Russian Mathematical Surveys, 2006, 61:2, 195–253

Bibliographic databases:

UDC: 510.67
MSC: 68P15, 03B70
Received: 03.06.2004

Citation: S. M. Dudakov, M. A. Taitslin, “Collapse results for query languages in database theory”, Uspekhi Mat. Nauk, 61:2(368) (2006), 3–66; Russian Math. Surveys, 61:2 (2006), 195–253

Citation in format AMSBIB
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\pages 3--66
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. M. Dudakov, “Pseudofinite Homogeneity, Isolation, and Reducibility”, Math. Notes, 81:4 (2007), 456–466  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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. M. A. Taitslin, “Comparison of expressive power of some query languages for databases”, Proc. Steklov Inst. Math., 274 (2011), 273–288  mathnet  crossref  mathscinet  isi  elib  elib
    4. S. M. Dudakov, “O granitsakh transfinitnogo postroeniya inflyatsionnoi nepodvizhnoi tochki”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2018, no. 3, 72–80  mathnet  crossref  elib
  • Успехи математических наук Russian Mathematical Surveys
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