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arXiv · 1607.03885

Good Frames in the Hart-Shelah Example

Will Boney·Sebastien Vasey
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Abstract

For a fixed natural number $n \geq 1$, the Hart-Shelah example is an abstract elementary class (AEC) with amalgamation that is categorical exactly in the infinite cardinals less than or equal to $\aleph_n$. We investigate recently-isolated properties of AECs in the setting of this example. We isolate the exact amount of type-shortness holding in the example and show that it has a type-full good $\aleph_{n-1}$-frame which fails the existence property for uniqueness triples. This gives the first example of such a frame. Along the way, we develop new tools to build and analyze good frames.

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Will Boney, Sebastien Vasey. 2016-07-13. Good Frames in the Hart-Shelah Example. https://doi.org/10.1007/s00153-017-0599-7

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