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...

• Type: Journal
• Year: 2008
• Where: JSYML
• Authors: John T. Baldwin, Saharon Shelah
• Keywords: Abstract Elementary Classes, Amalgamation Property, JSYML 2008, Whitehead Abelian Groups