Upward Stability Transfer for Tame Abstract Elementary Classes

, &
Notre Dame Journal of Formal Logic 47 (2):291-298 (2006)
  Copy   BIBTEX

Abstract

Grossberg and VanDieren have started a program to develop a stability theory for tame classes. We name some variants of tameness and prove the following. Let K be an AEC with Löwenheim-Skolem number ≤κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then K is Galois-stable in κ⁺ⁿ for all n<ω. With one further hypothesis we get a very strong conclusion in the countable case. Let K be an AEC satisfying the amalgamation property and with Löwenheim-Skolem number ℵ₀ that is ω-local and ℵ₀-tame. If K is ℵ₀-Galois-stable then K is Galois-stable in all cardinalities

Categories

Keywords

Reprint years

DOI

10.1305/ndjfl/1153858652

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,322

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Rank Functions and Partial Stability Spectra for Tame Abstract Elementary Classes.Michael J. Lieberman - 2013 - Notre Dame Journal of Formal Logic 54 (2):153-166.
Shelah's Categoricity Conjecture from a Successor for Tame Abstract Elementary Classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Symbolic Logic 71 (2):553 - 568.
Upward Categoricity from a Successor Cardinal for Tame Abstract Classes with Amalgamation.Olivier Lessmann - 2005 - Journal of Symbolic Logic 70 (2):639 - 660.
Categoricity from one successor cardinal in Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (2):181-201.
On Absoluteness of Categoricity in Abstract Elementary Classes.Sy-David Friedman & Martin Koerwien - 2011 - Notre Dame Journal of Formal Logic 52 (4):395-402.
Abstract Elementary Classes with Löwenheim-Skolem Number Cofinal with ω.Gregory M. Johnson - 2010 - Notre Dame Journal of Formal Logic 51 (3):361-371.
Elementary classes in basic modal logic.Holger Sturm - 2000 - Studia Logica 64 (2):193-213.
Diversity-stability hypothesis.Greg Mikkelson - manuscript
T-convexity and Tame extensions.LouDen Dries & Adam H. Lewenberg - 1995 - Journal of Symbolic Logic 60 (1):74 - 102.
Types in Abstract Elementary Classes.Tapani Hyttinen - 2004 - Notre Dame Journal of Formal Logic 45 (2):99-108.
Stability of nilpotent groups of class 2 and prime exponent.Alan H. Mekler - 1981 - Journal of Symbolic Logic 46 (4):781-788.
Une correspondance entre anneaux partiels et groupes.Patrick Simonetta - 1997 - Journal of Symbolic Logic 62 (1):60-78.
A group-theoretical invariant for elementary equivalence and its role in representations of elementary classes.Daniele Mundici - 1981 - Studia Logica 40 (3):253 - 267.

Analytics

Added to PP
2010-08-24

Downloads
41 (#377,987)

6 months
22 (#118,956)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

Forking and superstability in Tame aecs.Sebastien Vasey - 2016 - Journal of Symbolic Logic 81 (1):357-383.
Building independence relations in abstract elementary classes.Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (11):1029-1092.
Tameness and extending frames.Will Boney - 2014 - Journal of Mathematical Logic 14 (2):1450007.
Toward a stability theory of tame abstract elementary classes.Sebastien Vasey - 2018 - Journal of Mathematical Logic 18 (2):1850009.
Downward categoricity from a successor inside a good frame.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (3):651-692.

View all 18 citations / Add more citations

References found in this work

Galois-stability for Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
Categoricity for abstract classes with amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.

Add more references