Rank functions for stable diagrams
Matematičeskie trudy, Tome 22 (2019) no. 1, pp. 119-126
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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.
@article{MT_2019_22_1_a4,
author = {K. Zh. Kudaǐbergenov},
title = {Rank functions for stable diagrams},
journal = {Matemati\v{c}eskie trudy},
pages = {119--126},
year = {2019},
volume = {22},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_2019_22_1_a4/}
}
K. Zh. Kudaǐbergenov. Rank functions for stable diagrams. Matematičeskie trudy, Tome 22 (2019) no. 1, pp. 119-126. http://geodesic.mathdoc.fr/item/MT_2019_22_1_a4/
[1] Kudaibergenov K. Zh., “Odnorodnye modeli i stabilnye diagrammy”, Sib. matem. zhurn., 43:5 (2002), 1064–1076 | MR
[2] Hyttinen T., Lessmann O., “A rank for the class of elementary submodels of a superstable homogeneous model”, J. Symbolic Logic, 67:4 (2002), 1469–1482 | DOI | MR | Zbl
[3] Shelah S., “Finite diagrams stable in power”, Ann. Math. Logic, 2 (1970), 69–118 | DOI | MR | Zbl