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JOURNALS // Matematicheskie Trudy // Archive

Mat. Tr., 2019 Volume 22, Number 1, Pages 119–126 (Mi mt350)

This article is cited in 1 paper

Rank functions for stable diagrams

K. Zh. Kudaĭbergenovab

a Department of Economics, KIMEP University, Almaty, 050010 Kazakhstan
b Institute of Mathematics and Mathematical Modeling, Almaty, 050010 Kazakhstan

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 $\infty$ then the diagram is stable; (2) if the diagram $D$ is stable then the set of non-algebraic types of rank less than $\infty$ is large enough.

Key words: homogeneous model, rank, stable diagram.

UDC: 510.67

Received: 26.01.2018
Revised: 04.05.2018
Accepted: 23.05.2018

DOI: 10.33048/mattrudy.2019.22.105


 English version:
Siberian Advances in Mathematics, 2020, 30:1, 21–25

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© Steklov Math. Inst. of RAS, 2024