Translator Disclaimer
September 2008 Examples of non-locality
John T. Baldwin, Saharon Shelah
J. Symbolic Logic 73(3): 765-782 (September 2008). DOI: 10.2178/jsl/1230396746

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 (ℵ0,ℵ1)-tame but is (20,∞)-tame; Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not (≤ℵ2,≤ℵ2)-compact.

Citation

Download Citation

John T. Baldwin. Saharon Shelah. "Examples of non-locality." J. Symbolic Logic 73 (3) 765 - 782, September 2008. https://doi.org/10.2178/jsl/1230396746

Information

Published: September 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1162.03017
MathSciNet: MR2444267
Digital Object Identifier: 10.2178/jsl/1230396746

Rights: Copyright © 2008 Association for Symbolic Logic

JOURNAL ARTICLE
18 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.73 • No. 3 • September 2008
Back to Top