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Examples of non-locality

  • John T. Baldwin (a1) (a2) and Saharon Shelah (a2) (a3)


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 (, ∞)-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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[BCG+00]Baldwin, J., Calvert, W., Goodrick, J., Villaveces, A., and Walczak-Typke, A., Abelian groups as aec's, preprint, 200?
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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