Upward Stability Transfer for Tame Abstract Elementary Classes
Baldwin, John ; Kueker, David ; VanDieren, Monica
Notre Dame J. Formal Logic, Tome 47 (2006) no. 1, p. 291-298 / Harvested from Project Euclid
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Grossberg and VanDieren have started a program to develop a stability theory for tame classes. We name some variants of tameness and prove the following. Let K be an AEC with Löwenheim-Skolem number ≤κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then K is Galois-stable in κ⁺ⁿ for all n<ω. With one further hypothesis we get a very strong conclusion in the countable case. Let K be an AEC satisfying the amalgamation property and with Löwenheim-Skolem number ℵ₀ that is ω-local and ℵ₀-tame. If K is ℵ₀-Galois-stable then K is Galois-stable in all cardinalities.
Publié le : 2006-04-14
Classification:  stability theory,  tameness,  abstract elementary class,  03C45,  03C52,  03C75,  03C05,  03C55,  03C95 
@article{1153858652,
     author = {Baldwin, John and Kueker, David and VanDieren, Monica},
     title = {Upward Stability Transfer for Tame Abstract Elementary Classes},
     journal = {Notre Dame J. Formal Logic},
     volume = {47},
     number = {1},
     year = {2006},
     pages = { 291-298},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1153858652}
}

Baldwin, John; Kueker, David; VanDieren, Monica. Upward Stability Transfer for Tame Abstract Elementary Classes. Notre Dame J. Formal Logic, Tome 47 (2006) no. 1, pp.  291-298. http://gdmltest.u-ga.fr/item/1153858652/