Examples of non-locality

被引:22
作者
Baldwin, John T. [1 ]
Shelah, Saharon [2 ,3 ]
机构
[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA
[2] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel
[3] Rutgers State Univ, Dept Math, New Brunswick, NJ 08854 USA
关键词
D O I
10.2178/jsl/1230396746
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We use kappa-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 (N-0. N-1)-tame but is (2(N0), infinity)-tame: Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not (<= N-2, <= N-2)-compact.
引用
收藏
页码:765 / 782
页数:18
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