Abstract
Let D be the diagram of a sufficiently homogeneous model. For types that are realized in this model, we introduce certain rank functions and prove the following assertions: (1) If, for each type, the rank is less than ∞ then the diagram is stable; (2) if the diagram D is stable then the set of non-algebraic types of rank less than ∞ is large enough.
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References
T. Hyttinen and O. Lessmann, “A rank for the class of elementary submodels of a superstable homogeneous model,” J. Symbolic Logic 67, 1469 (2002).
K. Zh. Kudaĭbergenov, “Homogeneous models and stable diagrams,” Sib. Matem. Zh. 43, 1064 (2002) [Siberian Math. J. 43, 858 (2002)].
S. Shelah, “Finite diagrams stable in power,” Ann. Math. Logic 2, 69 (1970).
Funding
The work was partially supported by the Ministry of Education and Science of the Republic of Kazakhstan (grant AP05130852).
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Russian Text © The Author(s), 2019, published in Matematicheskie Trudy, 2019, Vol. 22, No. 1, pp. 119–126.
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Kudaĭbergenov, K.Z. Rank Functions for Stable Diagrams. Sib. Adv. Math. 30, 21–25 (2020). https://doi.org/10.3103/S1055134420010022
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DOI: https://doi.org/10.3103/S1055134420010022