Submission date:

Abstract:

For a fixed natural number n ≥ 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 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.

Mathematics Subject Classification: 03C48 (Primary), 03C45, 03C52, 03C55 (Secondary)

Keywords and phrases: Abstract elementary classes; Hart-Shelah example; Good frames; Uniqueness triples

Full text arXiv 1607.03885: pdf, ps.