252 research outputs found
Galois-stability for Tame Abstract Elementary Classes
We introduce tame abstract elementary classes as a generalization of all
cases of abstract elementary classes that are known to permit development of
stability-like theory. In this paper we explore stability results in this
context. We assume that \K is a tame abstract elementary class satisfying the
amalgamation property with no maximal model. The main results include:
(1) Galois-stability above the Hanf number implies that \kappa(K) is less
than the Hanf number. Where \kappa(K) is the parallel of \kapppa(T) for f.o. T.
(2) We use (1) to construct Morley sequences (for non-splitting) improving
previous results of Shelah (from Sh394) and Grossberg & Lessmann.
(3) We obtain a partial stability-spectrum theorem for classes categorical
above the Hanf number.Comment: 23 page
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
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