Good Frames in the Hart-Shelah Example

Abstract

For a fixed natural number $n\ge 1$, 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.

24 pages

References in corpus (5)

• Building independence relations in abstract elementary classes
• Infinitary stability theory
• Downward categoricity from a successor inside a good frame
• Superstability from categoricity in abstract elementary classes
• Symmetry in abstract elementary classes with amalgamation

Cited by in corpus (2)

• Abstract elementary classes stable in ${\aleph }_0$
• Tameness from two successive good frames