Examples of non-locality

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Examples of non-locality
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 (0, 1)-tame but is (20 , )tame; Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not ( 2, 2)-compact. A primary object of study in first order model theory is a syntactic type: the type of a over B in a model N is the collection of formulas (x, b) which are true of a in N. Usually the N is suppressed because a preliminary construction has established a universal domai...
John T. Baldwin, Saharon Shelah
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Authors John T. Baldwin, Saharon Shelah
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