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Preprint Number 907

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907. Will Boney, Monica M. VanDieren
Limit Models in Strictly Stable Abstract Elementary Classes
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Submission date: 19 August 2015.

Abstract:

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 K is an abstract elementary class satisfying
1. the joint embedding and amalgamation properties with no maximal model of cardinality μ.
2. stability in μ.
3. κ_{μ}(K)<μ^+.
4. continuity for non-μ-splitting (i.e. if p in gS(M) and M is a limit model witnessed by < M_i | i<α > for some limit ordinal α < μ^+ and there exists N so that p \restriction M_i does not μ-split over N for all i<α, then p does not μ-split over N).
For θ and δ limit ordinals <μ^+ both with cofinality ≥ κ_{μ}(K), if K satisfies symmetry for non-μ-splitting (or just (μ,δ)-symmetry), then, for any M_1 and M_2 that are (μ,θ) and (μ,δ)-limit models over M_0, respectively, we have that M_1 and M_2 are isomorphic over M_0.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1508.04717: pdf, ps.


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