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arXiv · 1507.01989

Union of Saturated Models in Superstable Abstract Elementary Classes

Monica M. VanDieren
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Abstract

In this paper we prove: Theorem 1. Let $\mathcal{K}$ be an abstract elementary class which satisfies the joint embedding and amalgamation properties. Suppose $\lambda>\mu\geq LS(\mathcal{K})$ and $\theta$ is a limit ordinal $<\lambda^+$. If $\mathcal{K}$ is $\mu$ superstable and $\mu^+$-superstable and satisfies $\mu^+$-symmetry, then for any increasing sequence $\langle M_i\mid i<\theta\rangle$ of $\mu^+$-saturated models of cardinality $\lambda$, the model $\bigcup_{i<\theta}M_i$ is $\mu^+$-saturated.

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Monica M. VanDieren. 2015-07-07. Union of Saturated Models in Superstable Abstract Elementary Classes. https://doi.org/10.13140/rg.2.1.3405.9367

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