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Transactions of the American Mathematical Society

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Stable finitely homogeneous structures


Authors: G. Cherlin and A. H. Lachlan
Journal: Trans. Amer. Math. Soc. 296 (1986), 815-850
MSC: Primary 03C10; Secondary 03C45, 20B99
DOI: https://doi.org/10.1090/S0002-9947-1986-0846608-8
MathSciNet review: 846608
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Abstract: Let $ L$ be a finite relational language and $ \operatorname{Hom}(L,\omega)$ denote the class of countable $ L$-structures which are stable and homogeneous. The main result of the paper is that there exists a natural number $ c(L)$ such that for any transitive $ \mathcal{M} \in \operatorname{Hom}(L;\omega)$, if $ E$ is a maximal 0-definable equivalence relation on $ \mathcal{M}$, then either $ \vert\mathcal{M}/E\vert < c(L)$, or $ \mathcal{M}/E$ is coordinatizable. In an earlier paper the second author analyzed certain subclasses $ \operatorname{Hom}(L, r)\ (r < \omega)$ of $ \operatorname{Hom}(L,\omega)$ for all sufficiently small $ r$. Thus the earlier analysis now applies to $ \operatorname{Hom}(L,\omega)$.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0846608-8
Article copyright: © Copyright 1986 American Mathematical Society

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