Good Frames in the Hart-shelah Example

Abstract

For a fixed natural number n ≥ 1, the Hart-Shelah example is an abstract elementary class (AEC) with amalgamation that is categorical exactlyelementary class (AEC) with amalgamation that is categorical exactly in the infinite cardinals less than or equal to אn. 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 אn−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.

Cite this paper

@inproceedings{Boney2017GoodFI, title={Good Frames in the Hart-shelah Example}, author={Will Boney and shelahaecbook and Sebastien Vasey}, year={2017} }