Rank functions and partial stability spectra for tame AECs

Details Rank functions and partial stability spectra for tame AECs Rank functions and partial stability spectra for tame AECs

2010-01-05

arxiv.org/abs/1001.0624v1

Mathematics

Logic

15 pages

Scientific paper

We introduce a family of rank functions and related notions of total transcendence for Galois types in abstract elementary classes. We focus, in particular, on abstract elementary classes satisfying the condition know as tameness (currently suspected to be a necessary condition for the development of a reasonable classification theory) where the connections between stability and total transcendence are most evident. As a byproduct, we obtain a partial upward stability transfer result for tame abstract elementary classes stable in a cardinal lambda satisfying lambda^{aleph_0}, a substantial generalization of a result of Baldwin, Kueker, and VanDieren.

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