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This article is cited in 1 scientific paper (total in 1 paper)
Pseudofinite Homogeneity, Isolation, and Reducibility
S. M. Dudakov Tver State University
Abstract:
It has been proved (by S. M. Dudakov and M. A. Taitslin) that the reducibility of some models of a theory implies the second pseudofinite homogeneity property for this theory. We prove the converse, namely, that any theory with the first or the second pseudofinite homogeneity property has a reducible model and, therefore, possesses the second isolation property. This also proves the equivalence of the second isolation property and the second pseudofinite homogeneity property, in contrast to the first pseudofinite homogeneity property, which is more general than the first isolation property (this was established by O. V. Belegradek, A. P. Stolboushin, and M. A. Taitslin).
Keywords:
reducible model, first and second pseudofinite homogeneity properties, second isolation property, query language, order collapse property, relational database.
Received: 26.04.2006
Citation:
S. M. Dudakov, “Pseudofinite Homogeneity, Isolation, and Reducibility”, Mat. Zametki, 81:4 (2007), 515–527; Math. Notes, 81:4 (2007), 456–466
Linking options:
https://www.mathnet.ru/eng/mzm3694https://doi.org/10.4213/mzm3694 https://www.mathnet.ru/eng/mzm/v81/i4/p515
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Abstract page: | 336 | Full-text PDF : | 180 | References: | 66 | First page: | 2 |
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