Superstability from categoricity in abstract elementary classes
| Autor: | Boney, Will, Grossberg, Rami, VanDieren, Monica M., Vasey, Sebastien |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Annals of Pure and Applied Logic 168 (2017), no. 7, 1383-1395 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.apal.2017.01.005 |
| Popis: | Starting from an abstract elementary class with no maximal models, Shelah and Villaveces have shown (assuming instances of diamond) that categoricity implies a superstability-like property for a certain independence relation called nonsplitting. We generalize their result as follows: given an abstract notion of independence for Galois (orbital) types over models, we derive that the notion satisfies a superstability property provided that the class is categorical and satisfies a weakening of amalgamation. This extends the Shelah-Villaveces result (the independence notion there was splitting) as well as a result of the first and second author where the independence notion was coheir. The argument is in ZFC and fills a gap in the Shelah-Villaveces proof. Comment: 14 pages |
| Databáze: | arXiv |
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