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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.

MSC:

03C45 Classification theory, stability, and related concepts in model theory
05B30 Other designs, configurations
51D20 Combinatorial geometries and geometric closure systems
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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
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