Examples of non-locality

John T. Baldwin*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)765-782
Number of pages18
JournalJournal of Symbolic Logic
Volume73
Issue number3
DOIs
StatePublished - Sep 2008
Externally publishedYes

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