28 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
An NIP-like Notion in Abstract Elementary Classes
This paper is a contribution to "neo-stability" type of result for abstract
elementary classes. Under certain set theoretic assumptions, we propose a
definition and a characterization of NIP in AECs. The class of AECs with NIP
properly contains the class of stable AECs. We show that for an AEC and
, is NIP if and only if there is a notion of
nonforking on it which we call a w*-good frame. On the other hand, the negation
of NIP leads to being able to encode subsets