10 research outputs found
Limit Models in Strictly Stable Abstract Elementary Classes
In this paper, we examine the locality condition for non-splitting and
determine the level of uniqueness of limit models that can be recovered in some
stable, but not superstable, abstract elementary classes. In particular we
prove:
Suppose that is an abstract elementary class satisfying
1. the joint embedding and amalgamation properties with no maximal model of
cardinality .
2. stabilty in .
3. .
4. continuity for non--splitting (i.e. if and is a
limit model witnessed by for some limit
ordinal and there exists so that does
not -split over for all , then does not -split over
).
For and limit ordinals both with cofinality , if satisfies symmetry for non--splitting (or just
-symmetry), then, for any and that are
and -limit models over , respectively, we have that
and are isomorphic over .Comment: This article generalizes some results from arXiv:1507.0199
Potential isomorphism of elementary substructures of a strictly stable homogeneous model
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