TY - JOUR
T1 - Examples of non-locality
AU - Baldwin, John T.
AU - Shelah, Saharon
PY - 2008/9
Y1 - 2008/9
N2 - 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 (N0, N1)-tame but is (2N0, ∞)-tame; Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not (≤ N2, ≤ N2-compact.
AB - 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 (N0, N1)-tame but is (2N0, ∞)-tame; Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not (≤ N2, ≤ N2-compact.
UR - http://www.scopus.com/inward/record.url?scp=52049101186&partnerID=8YFLogxK
U2 - 10.2178/jsl/1230396746
DO - 10.2178/jsl/1230396746
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AN - SCOPUS:52049101186
SN - 0022-4812
VL - 73
SP - 765
EP - 782
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 3
ER -