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  1.  13
    Non-Forking Frames in Abstract Elementary Classes.Adi Jarden & Saharon Shelah - 2013 - Annals of Pure and Applied Logic 164 (3):135-191.
    The stability theory of first order theories was initiated by Saharon Shelah in 1969. The classification of abstract elementary classes was initiated by Shelah, too. In several papers, he introduced non-forking relations. Later, Shelah [17, II] introduced the good non-forking frame, an axiomatization of the non-forking notion.We improve results of Shelah on good non-forking frames, mainly by weakening the stability hypothesis in several important theorems, replacing it by the almost λ-stability hypothesis: The number of types over a model of cardinality (...)
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  2.  10
    Tameness, Uniqueness Triples and Amalgamation.Adi Jarden - 2016 - Annals of Pure and Applied Logic 167 (2):155-188.
  3.  12
    Independence, Dimension and Continuity in Non-Forking Frames.Adi Jarden & Alon Sitton - 2013 - Journal of Symbolic Logic 78 (2):602-632.
    The notion $J$ is independent in $(M,M_0,N)$ was established by Shelah, for an AEC (abstract elementary class) which is stable in some cardinal $\lambda$ and has a non-forking relation, satisfying the good $\lambda$-frame axioms and some additional hypotheses. Shelah uses independence to define dimension. Here, we show the connection between the continuity property and dimension: if a non-forking satisfies natural conditions and the continuity property, then the dimension is well-behaved. As a corollary, we weaken the stability hypothesis and two additional (...)
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