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arXiv · 1509.07024

Building prime models in fully good abstract elementary classes

Sebastien Vasey
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Abstract

We show how to build primes models in classes of saturated models of abstract elementary classes (AECs) having a well-behaved independence relation: $\mathbf{Theorem.}$ Let $K$ be an almost fully good AEC that is categorical in $\text{LS} (K)$ and has the $\text{LS} (K)$-existence property for domination triples. For any $λ> \text{LS} (K)$, the class of Galois saturated models of $K$ of size $λ$ has prime models over every set of the form $M \cup \{a\}$. This generalizes an argument of Shelah, who proved the result when $λ$ is a successor cardinal.

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Sebastien Vasey. 2016-05-10. Building prime models in fully good abstract elementary classes. https://doi.org/10.1002/malq.201600025

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