Geodesic
Pseudofinite Homogeneity, Isolation, and Reducibility
Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 515-527

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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. 
@article{MZM_2007_81_4_a4,
     author = {S. M. Dudakov},
     title = {Pseudofinite {Homogeneity,} {Isolation,} and {Reducibility}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {515--527},
     publisher = {mathdoc},
     volume = {81},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a4/}
}
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S. M. Dudakov. Pseudofinite Homogeneity, Isolation, and Reducibility. Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 515-527. http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a4/