Journal of Symbolic Logic 73 (3):765-782 (2008)

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Abstract
We use κ-free but not Whitehead Abelian groups to constructElementary Classes (AEC) which satisfy the amalgamation property but fail various conditions on the locality of Galois-types. We introduce the notion that an AEC admits intersections. We conclude that for AEC which admit intersections, the amalgamation property can have no positive effect on locality: there is a transformation of AEC's which preserves non-locality but takes any AEC which admits intersections to one with amalgamation. More specifically we have: Theorem 5.3. There is an AEC with amalgamation which is not (N₀, N₁)-tame but is 2(N0, ∞)-tame; Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not (≤ N₂, ≤ N₂)-compact
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DOI 10.2178/jsl/1230396746
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References found in this work BETA

Categoricity for Abstract Classes with Amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
Galois-Stability for Tame Abstract Elementary Classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
Independence in Finitary Abstract Elementary Classes.Tapani Hyttinen & Meeri Kesälä - 2006 - Annals of Pure and Applied Logic 143 (1-3):103-138.

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Citations of this work BETA

Shelah's Eventual Categoricity Conjecture in Universal Classes: Part I.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (9):1609-1642.
Building Independence Relations in Abstract Elementary Classes.Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (11):1029-1092.
Algebraic Description of Limit Models in Classes of Abelian Groups.Marcos Mazari-Armida - 2020 - Annals of Pure and Applied Logic 171 (1):102723.
Categoricity in Multiuniversal Classes.Nathanael Ackerman, Will Boney & Sebastien Vasey - 2019 - Annals of Pure and Applied Logic 170 (11):102712.
Tameness and Extending Frames.Will Boney - 2014 - Journal of Mathematical Logic 14 (2):1450007.

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