Sudoplatov, S. V. Transitive arrangements of algebraic systems. (English. Russian original) Zbl 0957.03042 Sib. Math. J. 40, No. 6, 1142-1145 (1999); translation from Sib. Mat. Zh. 40, No. 6, 1347-1351 (1999). The author introduces the notion of a transitive arrangement \(T^{\ast}\) of a countable family of complete predicative theories \(T_{i}\), \(i\in\omega\), which are Morley expanded, in an exact pseudoplane. The theory \(T^{\ast}\) is transitive. Moreover, \(T^{\ast}\) is stable (superstable, \(\omega\)-stable, small, an \(n\)-theory) if and only if so are all of \(T_{i}\), \(i\in\omega\). The spectrum function of \(T^{\ast}\) is calculated. Reviewer: A.N.Ryaskin (Novosibirsk) Cited in 3 Documents MSC: 03C45 Classification theory, stability, and related concepts in model theory 05B30 Other designs, configurations 51D20 Combinatorial geometries and geometric closure systems Keywords:transitive arrangement; exact pseudoplane; stable theory; superstable theory; \(\omega \)-stable theory; small theory; \(n\)-theory PDFBibTeX XMLCite \textit{S. V. Sudoplatov}, Sib. Math. J. 40, No. 6, 1347--1351 (1999; Zbl 0957.03042); translation from Sib. Mat. Zh. 40, No. 6, 1347--1351 (1999) Full Text: DOI References: [1] S. V. Sudoplatov, ”On trigonometries of groups on a projective plane,” Sibirsk. Mat. Zh.,36, No. 2, 419–431 (1995). · Zbl 0863.51010 [2] Handbook of Mathematical Logic. Vol. 1: Model Theory [Russian translation], Nauka, Moscow (1982). [3] A. Pillay, An Introduction to Stability Theory, Oxford Univ. Press, Oxford (1983). · Zbl 0526.03014 [4] A. Pillay, ”Stable theories, pseudoplanes and the number of countable models,” Ann. Pure Appl. Logic,43, No. 2, 147–160 (1989). · Zbl 0676.03024 · doi:10.1016/0168-0072(80)90002-0 [5] S. V. Sudoplatov, ”On a certain complexity estimate in graph theories,” Sibirsk. Mat. Zh.,37, No. 3, 700–703 (1996). · Zbl 0874.03044 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.