Categoricity and closure of amalgamation bases under unions
Let be an abstract elementary class, let be its Hanf number, and let be its Löwenheim–Skolem number. For a cardinal , let be the class of amalgamation bases in of cardinality . Closure conjecture for amalgamation bases. If there exists a such that is categorical in , then is closed under unions of length for all with . This is presented as a weakening of Grossberg's Intermediate Categoricity Conjecture; the source does not give a resolution.
References
Primary source
Monica VanDieren, “Categoricity in Abstract Elementary Classes with No Maximal Models”, arXiv:math/0510579 (2005).
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