Journal of Symbolic Logic

Examples of non-locality

John T. Baldwin and Saharon Shelah

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We use κ-free but not Whitehead Abelian groups to construct Abstract Elementary 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 (ℵ0,ℵ1)-tame but is (20,∞)-tame; Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not (≤ℵ2,≤ℵ2)-compact.

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J. Symbolic Logic, Volume 73, Issue 3 (2008), 765-782.

First available in Project Euclid: 27 December 2008

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Baldwin, John T.; Shelah, Saharon. Examples of non-locality. J. Symbolic Logic 73 (2008), no. 3, 765--782. doi:10.2178/jsl/1230396746.

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